半波長ダイポールの電気力線

Mathematica 5.1で計算。
他のバージョン(例えば Mathematica 4.2)を使うとNDSolveルーチンが古いバージョンなので、FieldLineコマンド内で使っているNDSolveコマンドの影響で違った結果となる。

[参考文献]
*http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/smalldipole/field_lines.pdf
*寺沢寛一, 「自然科学者のための 数学概論」, 岩波書店
*K.W. Kark, and R. Dill, “A general theory on the graphical representation of antenna-radiation fields,” IEEE Trans. Antennas Propag., Vol.32, No.2, Feb. 1990.

2005/6/8 平野拓一(東京工業大学)
May 28, 2005 Takuichi Hirano (Tokyo Institute of Technology)

<< Graphics`Colors`

\( (*\ モ - メント法の結果\ *) \)
ivec = {{0.0015993914407161295`, -0.638326039248772`}, {0.0027831608122753076`, -0.6325631210094189`}, {0.003901425945848874`, -0.626899099492919`}, {0.004943792355583696`, -0.6210407749991087`}, {0.005915568720751507`, -0.6149339167612491`}, {0.006814306518962076`, -0.6085180370926005`}, {0.007635948282381321`, -0.6017301860351156`}, {0.008375699124354924`, -0.5944970505766951`}, {0.009028639464416678`, -0.586729335457548`}, {0.009590034347251829`, -0.5783140102107232`}, {0.01005550072072821`, -0.5691022309455882`}, {0.010421052498610209`, -0.5588863529252784`}, {0.010683083515825849`, -0.5473679964174963`}, {0.010837141645569558`, -0.5339289636856862`}, {0.010883995930053006`, -0.518519737056533`}, {0.010745778116230915`, -0.4873006127297302`}, {0.010883995930052999`, -0.518519737056533`}, {0.010837141645569539`, -0.5339289636856862`}, {0.01068308351582582`, -0.5473679964174962`}, {0.010421052498610183`, -0.5588863529252782`}, {0.010055500720728179`, -0.5691022309455882`}, {0.009590034347251798`, -0.578314010210723`}, {0.009028639464416646`, -0.586729335457548`}, {0.008375699124354883`, -0.594497050576695`}, {0.007635948282381277`, -0.6017301860351156`}, {0.006814306518962035`, -0.6085180370926004`}, {0.00591556872075147`, -0.6149339167612489`}, {0.004943792355583666`, -0.6210407749991085`}, {0.0039014259458488502`, -0.6268990994929189`}, {0.002783160812275291`, -0.6325631210094186`}, {0.00159939144071612`, -0.6383260392487717`}};

c = 1. ;
λ0 = 1. ;
k0 = ((2 π)/λ)0;
h = λ0/4;
nn = Length[ ivec ];
cur[n_, t_] := 
        ivec[[n, 1]]*Cos[t + ivec[[n, 2]]];

Clear[ω];
sol = 
        Solve[λ0*(ω/(2*π)) == 
            c, ω];
ω = (ω  /.  sol[[1]]);

grapdist = {Red, AbsoluteThickness[2], 
          Line[Table[{20*
                  ivec[[i, 
                      1]], ((i - 1)/(nn - 1))*(2*h) - 
                  h}, {i, 1, nn}]]};
Show[ Graphics[grapdist] ];

微小ダイポールの放射電界

\(\(r\&^ . x\&^ = 
        Sin[θ]\ Cos[φ];\)\)
\(\(θ\&^ . x\&^ = 
        Cos[θ]\ Cos[φ];\)\)
\(\(\(φ\&^ . x\&^ = Sin[φ];\)\(
\)
    \)\)
\(\(r\&^ . y\&^ = 
        Sin[θ]\ Sin[φ];\)\)
\(\(θ\&^ . y\&^ = 
        Cos[θ]\ Sin[φ];\)\)
\(\(\(φ\&^ . y\&^ = Cos[φ];\)\(
\)
    \)\)
\(\(r\&^ . z\&^ = Cos[θ];\)\)
\(\(θ\&^ . z\&^ = Sin[θ];\)\)
\(\(φ\&^ . z\&^ = 0;\)\)

\(\(\(simpi[f_, {ξ_, a_, b_}, n_] := 
        Module[{h = \((b - a)\)/\((2*n)\), x, i}, 
		x[i_] := 
            a + h*i; 
		\(h\/3\) \((\((f /. {ξ -> x[0]})\) + 
                  4\ \(∑\+\(i = 1\)\%n\((f /. {ξ -> 
                              x[2*i - 1]})\)\) + 
                  2\ \(∑\+\(i = 2\)\%n\((f /. {ξ -> \ 
                              x[2*i - 2]})\)\) + \((f /. {ξ -> \ 
                          x[2*n]})\))\) // N
	];\)\(
\)
    \)\)
er[i_, r_, θ_, t_] := 
        2*Cos[θ]*(Cos[k0*(c*t - r) + ivec[[i, 2]]]/(((k0*r))^2) + Sin[k0*(c*t - r) + ivec[[i, 2]]]/(((k0*r))^3));
etheta[i_, r_, θ_, t_] := 
        Sin[θ]*(Cos[k0*(c t - r) + ivec[[i, 2]]]/(((k0*r))^2) - ((1/((k0*r))) - (1/(((k0*r))^3)))*
                Sin[k0*(c t - r) + 
                    ivec[[i, 2]]]);
hphi[i_, r_, θ_, t_] := 
        Sin[θ]*(Cos[k0*(c*t - r) + ivec[[i, 2]]]/(k0*r) - 
              Sin[k0*(c*t - r) + ivec[[i, 2]]]/(((k0*r))^2));
ex[i_, r_, θ_, φ_, t_] := 
        Sin[θ]*Cos[φ]*er[i, r, θ, t] + 
          Cos[θ]*Cos[φ]*
            etheta[i, r, θ, t];
ey[i_, r_, θ_, φ_, t_] := 
        Sin[θ]*Sin[φ]*er[i, r, θ, t] + 
          Cos[θ]*Sin[φ]*
            etheta[i, r, θ, t];
ez[i_, r_, θ_, φ_, t_] := 
        Cos[θ]*er[i, r, θ, t] - 
          Sin[θ]*
            etheta[i, r, θ, t];
eField[xo_, yo_, zo_, t_] := 
        Module[{xs = 0, ys = 0, zs = 0, r, θ, φ, exsum = 0, 
            eysum = 0, 
            ezsum = 0}, 
Do[
zs = (i - 
                        1)/(nn - 1)*(2*h) - 
                h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
              ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
              ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
exsum += 
              ivec[[i, 1]]*
                ex[i, r, θ, φ, t]; 
eysum += 
              ivec[[i, 1]]*
                ey[i, r, θ, φ, t]; 
ezsum += 
              ivec[[i, 1]]*
                ez[i, r, θ, φ, t]
, {i, 1, 
              nn}
]; 
{exsum, eysum, 
            ezsum}
];
erSumSpherical[ro_, θo_, φo_, t_] := 
        Module[{xo = ro*Sin[θo]*Cos[φo], 
            yo = ro*Sin[θo]*Sin[φo], zo = ro*Cos[θo], 
            xs = 0, ys = 0, zs = 0, r, θ, φ, 
            erSum = 0}, 
Do[
zs = (i - 
                        1)/(nn - 1)*(2*h) - 
                h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
              ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
              ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
erSum += 
              ivec[[i, 1]]*er[i, r, θ, t];
, {i, 
              1, nn}
]; 
erSum
];
ethetaSumSpherical[ro_, θo_, φo_, t_] := 
        Module[{xo = ro*Sin[θo]*Cos[φo], 
            yo = ro*Sin[θo]*Sin[φo], zo = ro*Cos[θo], 
            xs = 0, ys = 0, zs = 0, r, θ, φ, 
            ethetaSum = 
              0}, 
Do[
zs = (i - 
                        1)/(nn - 1)*(2*h) - 
                h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
              
              ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
              ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
ethetaSum += 
              ivec[[i, 1]]*
                etheta[i, r, θ, t];
, {i, 1, 
              nn}
]; 
ethetaSum
];
hphiSumSpherical[ro_, θo_, φo_, t_] := 
        Module[{xo = ro*Sin[θo]*Cos[φo], 
            yo = ro*Sin[θo]*Sin[φo], zo = ro*Cos[θo], 
            xs = 0, ys = 0, zs = 0, r, θ, φ, 
            hphiSum = 
              0}, 
Do[
zs = (i - 
                        1)/(nn - 1)*(2*h) - 
                h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
              ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
              ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
hphiSum += 
              ivec[[i, 1]]*
                hphi[i, r, θ, t]
, {i, 1, 
              nn}
]; 
hphiSum
];
energy[xo_, yo_, zo_, t_] := 
      Module[{xs = 0, ys = 0, zs = 0, r, θ, φ, exsum = 0, 
          eysum = 0, 
          ezsum = 0}, 
Do[
zs = (i - 
                      1)/(nn - 1)*(2*h) - 
              h; 
r = (Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]); 
θ = 
            ArcCos[((zo - zs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2) + (((zo - zs))^2)]))]; 
φ = 
            ArcCos[((xo - xs)/(Sqrt[(((xo - xs))^2) + (((yo - ys))^2)]))]; 
exsum += 
            ivec[[i, 1]]*
              ex[i, r, θ, φ, t]; 
eysum += 
            ivec[[i, 1]]*
              ey[i, r, θ, φ, t]; 
ezsum += 
            ivec[[i, 1]]*
              ez[i, r, θ, φ, t]
, {i, 1, 
            nn}
]; 
(exsum^2) + (eysum^2) + 
          (ezsum^2)
]

FieldLines

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, 0][[2]];
eyFL = eField[0, x, y, 0][[3]];
eline1 = 
        Table[FieldLine[{x, exFL, xs}, {y, eyFL, 0.001}, {l, 500}], {xs, 0.1, 
            2, 0.1}];
eline2 = 
        Table[FieldLine[{x, -exFL, xs}, {y, eyFL, 0.001}, {l, 
              500}], {xs, -0.1, -2, -0.1}];
Table[
      Show[Graphics[{AbsoluteThickness[2], eline1, 
            eline2}], 
PlotRange -> {{-2, 
              2}, {-2, 2}}, 
AspectRatio -> 
          Automatic], {t, 
        0, (π/(c k0)) - 
          0.001*(π/(c k0)), (π/(c k0))/
          1}]

FieldLines (Ver.2)

t=0

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*0;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 0.9}]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.5826842652307703`;
x1 = 0.6364915772054781`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.3256727988737908`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.6123387772940403`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.3256727988737908`, 
0.40476973065831984`, 
0.43706439246878515`, 
0.462038839468198`, 
0.48337723709359487`, 
0.5024986472358345`, 
0.5201316361881106`, 
0.5367131824348096`, 
0.5525340867286397`, 
0.5678039074663213`, 
0.5826842652307703`, 
0.59730792310233`}, 
{0.8729080265910356`, 
0.9409125598989817`, 
0.9696754432728597`, 
0.9922198259543286`, 
1.0116601758651687`, 
1.0292032362614032`, 
1.0454719372051489`, 
1.0608419366168758`, 
1.075564665230958`, 
1.0898224369673402`, 
1.1037568053867375`, 
1.1174848719220616`, 
1.1311097218589836`}, 
{1.3858490584811256`, 
1.4523160289601091`, 
1.480504168286191`, 
1.5026247518368478`, 
1.5217167220114154`, 
1.5389578545449174`, 
1.5549562975078586`, 
1.5700789175970522`, 
1.5845713611572716`, 
1.5986118340742796`, 
1.6123387772940403`, 
1.6392967976364399`}, 
{1.8919429153611673`, 
1.9859013906843712`, 
2.0268434531162924`, 
2.059876648510935`, 
2.089315413485672`, 
2.116922959976108`}, 
{2.3954937708961714`, 
2.489137194553511`, 
2.529953180748686`, 
2.5628886875360957`, 
2.619773013444123`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*0;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*0;
eline1 = {{FieldLine[{x, exFL, 0.3256727988737908`}, {y, eyFL, 
                0}, {l, 20}], 
FieldLine[{x, exFL, 
                0.40476973065831984`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, exFL, 
                0.43706439246878515`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, exFL, 
                0.462038839468198`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, exFL, 
                0.48337723709359487`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, exFL, 
                0.5024986472358345`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, exFL, 
                0.5201316361881106`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, exFL, 
                0.5367131824348096`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.5367131824348096`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.5525340867286397`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.5525340867286397`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.5678039074663213`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, 
                0.5678039074663213`}, {y, -eyFL, 0}, {l, 
                20}], 
FieldLine[{x, exFL, 
                0.5826842652307703`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, 
                0.5826842652307703`}, {y, -eyFL, 0}, {l, 
                20}], 
FieldLine[{x, exFL, 
                0.59730792310233`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, -exFL, 
                0.59730792310233`}, {y, -eyFL, 0}, {l, 
                25}]}, 
{FieldLine[{x, exFL, 
                0.8729080265910356`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, exFL, 
                0.9409125598989817`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, exFL, 
                0.9696754432728597`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, exFL, 
                0.9922198259543286`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, exFL, 
                1.0116601758651687`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, exFL, 
                1.0292032362614032`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, exFL, 
                1.0454719372051489`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, exFL, 
                1.0608419366168758`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.075564665230958`}, {y, eyFL, 0}, {l, 
                145}], 
FieldLine[{x, exFL, 
                1.0898224369673402`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.1037568053867375`}, {y, eyFL, 0}, {l, 
                185}], 
FieldLine[{x, exFL, 
                1.1174848719220616`}, {y, eyFL, 0}, {l, 
                230}]}, 
{FieldLine[{x, exFL, 
                1.3858490584811256`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, exFL, 
                1.4523160289601091`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, exFL, 
                1.480504168286191`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, exFL, 
                1.5026247518368478`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, exFL, 
                1.5217167220114154`}, {y, eyFL, 0}, {l, 
                255}], 
FieldLine[{x, exFL, 
                1.5389578545449174`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.5549562975078586`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, exFL, 
                1.5700789175970522`}, {y, eyFL, 0}, {l, 
                315}], 
FieldLine[{x, exFL, 
                1.5845713611572716`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, exFL, 
                1.5986118340742796`}, {y, eyFL, 0}, {l, 
                380}], 
FieldLine[{x, exFL, 
                1.6123387772940403`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, exFL, 
                1.6258667859087184`}, {y, eyFL, 0}, {l, 
                530}]}, 
{FieldLine[{x, exFL, 
                1.8919429153611673`}, {y, eyFL, 0}, {l, 
                420}], 
FieldLine[{x, exFL, 
                1.9859013906843712`}, {y, eyFL, 0}, {l, 
                420}], 
FieldLine[{x, exFL, 
                2.0268434531162924`}, {y, eyFL, 0}, {l, 
                470}], 
FieldLine[{x, exFL, 
                2.059876648510935`}, {y, eyFL, 0}, {l, 
                530}], 
FieldLine[{x, exFL, 
                2.089315413485672`}, {y, eyFL, 0}, {l, 
                630}], 
FieldLine[{x, exFL, 
                2.116922959976108`}, {y, eyFL, 0}, {l, 
                790}]}, 
{FieldLine[{x, exFL, 
                2.5628886875360957`}, {y, eyFL, 0}, {l, 
                840}], 
FieldLine[{x, exFL, 
                2.5922429492187247`}, {y, eyFL, 0}, {l, 
                990}], 
FieldLine[{x, exFL, 
                2.619773013444123`}, {y, eyFL, 0}, {l, 
                1260}]}, 
{FieldLine[{x, exFL, 
                3.1217163280744566`}, {y, eyFL, 0}, {l, 
                1840}]}};
eline2 = {{FieldLine[{x, -exFL, -0.3256727988737908`}, {y, 
                eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, -0.40476973065831984`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, -0.43706439246878515`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, -exFL, -0.462038839468198`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, -exFL, -0.48337723709359487`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, -exFL, -0.5024986472358345`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, -exFL, -0.5201316361881106`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, -0.5367131824348096`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.5367131824348096`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.5525340867286397`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.5525340867286397`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.5678039074663213`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, 
                exFL, -0.5678039074663213`}, {y, -eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, -0.5826842652307703`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, 
                exFL, -0.5826842652307703`}, {y, -eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, -0.59730792310233`}, {y, eyFL, 0}, {l, 
                25}], 
FieldLine[{x, 
                exFL, -0.59730792310233`}, {y, -eyFL, 0}, {l, 
                25}]}, 
{FieldLine[{x, -exFL, -0.8729080265910356`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, -exFL, -0.9409125598989817`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, -exFL, -0.9696754432728597`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, -exFL, -0.9922198259543286`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, -exFL, -1.0116601758651687`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, -exFL, -1.0292032362614032`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, -exFL, -1.0454719372051489`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, -exFL, -1.0608419366168758`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.075564665230958`}, {y, eyFL, 0}, {l, 
                145}], 
FieldLine[{x, -exFL, -1.0898224369673402`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.1037568053867375`}, {y, eyFL, 0}, {l, 
                185}], 
FieldLine[{x, -exFL, -1.1174848719220616`}, {y, eyFL, 0}, {l, 
                230}]}, 
{FieldLine[{x, -exFL, -1.3858490584811256`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, -exFL, -1.4523160289601091`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, -exFL, -1.480504168286191`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, -exFL, -1.5026247518368478`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, -exFL, -1.5217167220114154`}, {y, eyFL, 0}, {l, 
                255}], 
FieldLine[{x, -exFL, -1.5389578545449174`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.5549562975078586`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, -exFL, -1.5700789175970522`}, {y, eyFL, 0}, {l, 
                315}], 
FieldLine[{x, -exFL, -1.5845713611572716`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, -exFL, -1.5986118340742796`}, {y, eyFL, 0}, {l, 
                380}], 
FieldLine[{x, -exFL, -1.6123387772940403`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, -exFL, -1.6258667859087184`}, {y, eyFL, 0}, {l, 
                530}]}, 
{FieldLine[{x, -exFL, -1.8919429153611673`}, {y, eyFL, 0}, {l, 
                420}], 
FieldLine[{x, -exFL, -1.9859013906843712`}, {y, eyFL, 0}, {l, 
                420}], 
FieldLine[{x, -exFL, -2.0268434531162924`}, {y, eyFL, 0}, {l, 
                470}], 
FieldLine[{x, -exFL, -2.059876648510935`}, {y, eyFL, 0}, {l, 
                530}], 
FieldLine[{x, -exFL, -2.089315413485672`}, {y, eyFL, 0}, {l, 
                630}], 
FieldLine[{x, -exFL, -2.116922959976108`}, {y, eyFL, 0}, {l, 
                790}]}, 
{FieldLine[{x, -exFL, -2.5628886875360957`}, {y, eyFL, 0}, {l, 
                840}], 
FieldLine[{x, -exFL, -2.5922429492187247`}, {y, eyFL, 0}, {l, 
                
                990}], 
FieldLine[{x, -exFL, -2.619773013444123`}, {y, eyFL, 0}, {l, 
                1260}]}, 
{FieldLine[{x, -exFL, -3.1217163280744566`}, {y, eyFL, 0}, {l, 
                1840}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(1/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*1;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 0.4}]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.40000234499828846`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.6503826743935536`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.7033701143782579`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.42179132814814624`, 
0.47851518117477027`, 
0.5089140710404542`, 
0.5328211827669325`, 
0.5534147343518749`, 
0.5719636583085221`, 
0.5891313661086187`, 
0.605320580616942`, 
0.6208018213969596`, 
0.6357716133707085`, 
0.6503826743935536`, 
0.6647613850471802`}, 
{0.9377721237465125`, 
1.005447977287115`, 
1.034090680535593`, 
1.0565473873474789`, 
1.0759162625905994`, 
1.0933978138623766`, 
1.1096117982121603`, 
1.1249319924955612`, 
1.1396085944491945`, 
1.1538230464279957`, 
1.1677162454938574`, 
1.1814047683116302`}, 
{1.4493396279533126`, 
1.5157153719164367`, 
1.543868269641843`, 
1.56596244957754`, 
1.5850324432804896`, 
1.6022543281389492`, 
1.6182353819327464`, 
1.6333419512149576`, 
1.6478193379833506`, 
1.6618455016470886`, 
1.6755586945157`, 
1.6890733578597295`}, 
{1.954985808153293`, 
2.048891733525539`, 
2.0898129539716366`, 
2.1228300754690297`, 
2.1522549895764813`}, 
{2.458336209674162`, 
2.5519528492774444`, 
2.592757982608972`, 
2.6256850250529378`, 
2.6550319251481675`, 
2.682555206537513`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*1;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*1;
eline1 = {{FieldLine[{x, exFL, 0.47851518117477027`}, {y, eyFL, 
                0}, {l, 30}], 
FieldLine[{x, exFL, 
                0.5089140710404542`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, exFL, 
                0.5328211827669325`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, exFL, 
                0.5534147343518749`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, exFL, 
                0.5719636583085221`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, exFL, 
                0.5891313661086187`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, exFL, 
                0.605320580616942`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, exFL, 
                0.6208018213969596`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, exFL, 
                0.6357716133707085`}, {y, eyFL, 0}, {l, 
                45}], 
FieldLine[{x, exFL, 
                0.6503826743935536`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, 
                0.6503826743935536`}, {y, -eyFL, 0}, {l, 
                30}], 
FieldLine[{x, exFL, 
                0.6647613850471802`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, 
                0.6647613850471802`}, {y, -eyFL, 0}, {l, 
                35}]}, 
{FieldLine[{x, exFL, 
                0.9377721237465125`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, exFL, 
                1.005447977287115`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, exFL, 
                1.034090680535593`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, exFL, 
                1.0565473873474789`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, exFL, 
                1.0759162625905994`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, exFL, 
                1.0933978138623766`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.1096117982121603`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.1249319924955612`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, exFL, 
                1.1396085944491945`}, {y, eyFL, 0}, {l, 
                165}], 
FieldLine[{x, exFL, 
                1.1538230464279957`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.1677162454938574`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.1814047683116302`}, {y, eyFL, 0}, {l, 
                255}]}, 
{FieldLine[{x, exFL, 
                1.4493396279533126`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, exFL, 
                1.5157153719164367`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, exFL, 
                1.543868269641843`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, exFL, 
                1.56596244957754`}, {y, eyFL, 0}, {l, 
                265}], 
FieldLine[{x, exFL, 
                1.5850324432804896`}, {y, eyFL, 0}, {l, 
                280}], 
FieldLine[{x, exFL, 
                1.6022543281389492`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.6182353819327464`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, exFL, 
                1.6333419512149576`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, exFL, 
                1.6478193379833506`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, exFL, 
                1.6618455016470886`}, {y, eyFL, 0}, {l, 
                415}], 
FieldLine[{x, exFL, 
                1.6755586945157`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, exFL, 
                1.6890733578597295`}, {y, eyFL, 0}, {l, 
                580}]}, 
{FieldLine[{x, exFL, 
                1.954985808153293`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, exFL, 
                2.048891733525539`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, exFL, 
                2.0898129539716366`}, {y, eyFL, 0}, {l, 
                500}], 
FieldLine[{x, exFL, 
                2.1228300754690297`}, {y, eyFL, 0}, {l, 
                570}], 
FieldLine[{x, exFL, 
                2.1522549895764813`}, {y, eyFL, 0}, {l, 
                670}], 
FieldLine[{x, exFL, 
                2.179849879777399`}, {y, eyFL, 0}, {l, 
                850}]}, 
{FieldLine[{x, exFL, 
                2.458336209674162`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, exFL, 
                2.5519528492774444`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, exFL, 
                2.6256850250529378`}, {y, eyFL, 0}, {l, 
                890}], 
FieldLine[{x, exFL, 
                2.6550319251481675`}, {y, eyFL, 0}, {l, 
                1040}], 
FieldLine[{x, exFL, 
                2.682555206537513`}, {y, eyFL, 0}, {l, 
                1330}]}, 
{FieldLine[{x, exFL, 
                3.1844166236836937`}, {y, eyFL, 0}, {l, 
                1920}]}};
eline2 = {{FieldLine[{x, -exFL, -0.47851518117477027`}, {y, 
                eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, -0.5089140710404542`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, -0.5328211827669325`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, -0.5534147343518749`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, -exFL, -0.5719636583085221`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, -0.5891313661086187`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, -0.605320580616942`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, -exFL, -0.6208018213969596`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, -exFL, -0.6357716133707085`}, {y, eyFL, 0}, {l, 
                45}], 
FieldLine[{x, -exFL, -0.6503826743935536`}, {y, eyFL, 0}, {l, 
                30}], 
FieldLine[{x, 
                exFL, -0.6503826743935536`}, {y, -eyFL, 0}, {l, 
                
                30}], 
FieldLine[{x, -exFL, -0.6647613850471802`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, 
                exFL, -0.6647613850471802`}, {y, -eyFL, 0}, {l, 
                35}]}, 
{FieldLine[{x, -exFL, -0.9377721237465125`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, -exFL, -1.005447977287115`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, -exFL, -1.034090680535593`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, -exFL, -1.0565473873474789`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, -exFL, -1.0759162625905994`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, -exFL, -1.0933978138623766`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.1096117982121603`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.1249319924955612`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, -exFL, -1.1396085944491945`}, {y, eyFL, 0}, {l, 
                165}], 
FieldLine[{x, -exFL, -1.1538230464279957`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.1677162454938574`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.1814047683116302`}, {y, eyFL, 0}, {l, 
                255}]}, 
{FieldLine[{x, -exFL, -1.4493396279533126`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, -exFL, -1.5157153719164367`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, -exFL, -1.543868269641843`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, -exFL, -1.56596244957754`}, {y, eyFL, 0}, {l, 
                265}], 
FieldLine[{x, -exFL, -1.5850324432804896`}, {y, eyFL, 0}, {l, 
                280}], 
FieldLine[{x, -exFL, -1.6022543281389492`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.6182353819327464`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, -exFL, -1.6333419512149576`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, -exFL, -1.6478193379833506`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, -exFL, -1.6618455016470886`}, {y, eyFL, 0}, {l, 
                415}], 
FieldLine[{x, -exFL, -1.6755586945157`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, -exFL, -1.6890733578597295`}, {y, eyFL, 0}, {l, 
                580}]}, 
{FieldLine[{x, -exFL, -1.954985808153293`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, -exFL, -2.048891733525539`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, -exFL, -2.0898129539716366`}, {y, eyFL, 0}, {l, 
                500}], 
FieldLine[{x, -exFL, -2.1228300754690297`}, {y, eyFL, 0}, {l, 
                570}], 
FieldLine[{x, -exFL, -2.1522549895764813`}, {y, eyFL, 0}, {l, 
                670}], 
FieldLine[{x, -exFL, -2.179849879777399`}, {y, eyFL, 0}, {l, 
                850}]}, 
{FieldLine[{x, -exFL, -2.458336209674162`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, -exFL, -2.5519528492774444`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, -exFL, -2.6256850250529378`}, {y, eyFL, 0}, {l, 
                890}], 
FieldLine[{x, -exFL, -2.6550319251481675`}, {y, eyFL, 0}, {l, 
                1040}], 
FieldLine[{x, -exFL, -2.682555206537513`}, {y, eyFL, 0}, {l, 
                1330}]}, 
{FieldLine[{x, -exFL, -3.1844166236836937`}, {y, eyFL, 0}, {l, 
                1920}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(2/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*2;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 3.0}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.47137001019010805`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.11137468792739326`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.18246488948629438`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.007746640046742487`, 
0.018405041298872132`, 
0.0746247850414778`, 
0.11137468792739326`}, 
{0.47137001019010805`, 
0.544534304865613`, 
0.5750480021984988`, 
0.5988278592923875`, 
0.6192506111268778`, 
0.6376220765775271`, 
0.6546150340634312`, 
0.6706343665531647`, 
0.6859504409773776`, 
0.7007587894777939`, 
0.7152107829127295`, 
0.7294312458399684`}, 
{1.0023431869226649`, 
1.0697486303716495`, 
1.0982914518383011`, 
1.1206749398534748`, 
1.1399839040652335`, 
1.1574137369258988`, 
1.1735815891339774`, 
1.188859690153044`, 
1.2034972217257272`, 
1.2176749065803385`, 
1.231533098382144`, 
1.2451879381196944`}, 
{1.512748607836687`, 
1.5790439718379206`, 
1.6071656881666812`, 
1.629236457872938`, 
1.6482869344969315`, 
1.6654917015818393`, 
1.6814572710151943`, 
1.6965495313005405`, 
1.711013480932306`, 
1.7250268618252522`, 
1.7387277595776625`, 
1.7522304792498145`}, 
{2.017995148182311`, 
2.111853202978992`, 
2.1527553755376125`, 
2.185757782086846`, 
2.2151699988522813`, 
2.2427532725714014`}, 
{2.5211616997661994`, 
2.614753472504129`, 
2.6555485087368447`, 
2.6884676675144106`, 
2.717807704673631`, 
2.7453246573357206`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*2;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*2;
eline1 = {{FieldLine[{x, exFL, 0.007746640046742487`}, {y, eyFL, 
                0}, {l, 1}], 
FieldLine[{x, exFL, 
                0.018405041298872132`}, {y, eyFL, 0}, {l, 
                1}], 
FieldLine[{x, -exFL, 
                0.018405041298872132`}, {y, -eyFL, 0}, {l, 
                1}], 
FieldLine[{x, exFL, 
                0.0746247850414778`}, {y, eyFL, 0}, {l, 
                1}], 
FieldLine[{x, -exFL, 
                0.0746247850414778`}, {y, -eyFL, 0}, {l, 
                1}], 
FieldLine[{x, exFL, 
                0.11137468792739326`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.11137468792739326`}, {y, -eyFL, 0}, {l, 
                5}]}, 
{FieldLine[{x, exFL, 
                0.47137001019010805`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, exFL, 
                0.544534304865613`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, exFL, 
                0.5750480021984988`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, exFL, 
                0.5988278592923875`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, exFL, 
                0.6192506111268778`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, exFL, 
                0.6376220765775271`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, exFL, 
                0.6546150340634312`}, {y, eyFL, 0}, {l, 45}], 
            FieldLine[{x, exFL, 0.6706343665531647`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.6859504409773776`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.7007587894777939`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.7152107829127295`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, exFL, 
                0.7294312458399684`}, {y, eyFL, 0}, {l, 
                80}]}, 
{FieldLine[{x, exFL, 
                1.0023431869226649`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.0697486303716495`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.0982914518383011`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.1206749398534748`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, exFL, 
                1.1399839040652335`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.1574137369258988`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, exFL, 
                1.1735815891339774`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.188859690153044`}, {y, eyFL, 0}, {l, 
                170}], 
FieldLine[{x, exFL, 
                1.2034972217257272`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, exFL, 
                1.2176749065803385`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.231533098382144`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, exFL, 
                1.2451879381196944`}, {y, eyFL, 0}, {l, 
                290}]}, 
{FieldLine[{x, exFL, 
                1.512748607836687`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.5790439718379206`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.6071656881666812`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.629236457872938`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, exFL, 
                1.6482869344969315`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.6654917015818393`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, exFL, 
                1.6814572710151943`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, exFL, 
                1.6965495313005405`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, exFL, 
                1.711013480932306`}, {y, eyFL, 0}, {l, 
                410}], 
FieldLine[{x, exFL, 
                1.7250268618252522`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, exFL, 
                1.7387277595776625`}, {y, eyFL, 0}, {l, 
                520}], 
FieldLine[{x, exFL, 
                1.7522304792498145`}, {y, eyFL, 0}, {l, 
                630}]}, 
{FieldLine[{x, exFL, 
                2.017995148182311`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, exFL, 
                2.111853202978992`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, exFL, 
                2.1527553755376125`}, {y, eyFL, 0}, {l, 
                530}], 
FieldLine[{x, exFL, 
                2.185757782086846`}, {y, eyFL, 0}, {l, 
                600}], 
FieldLine[{x, exFL, 
                2.2151699988522813`}, {y, eyFL, 0}, {l, 
                710}], 
FieldLine[{x, exFL, 
                2.2427532725714014`}, {y, eyFL, 0}, {l, 
                900}]}, 
{FieldLine[{x, exFL, 
                2.6884676675144106`}, {y, eyFL, 0}, {l, 
                930}], 
FieldLine[{x, exFL, 
                2.717807704673631`}, {y, eyFL, 0}, {l, 
                1100}], 
FieldLine[{x, exFL, 
                2.7453246573357206`}, {y, eyFL, 0}, {l, 
                1390}]}};
eline2 = {{FieldLine[{x, -exFL, -0.007746640046742487`}, {y, 
                eyFL, 0}, {l, 
                1}], 
FieldLine[{x, -exFL, -0.018405041298872132`}, {y, eyFL, 0}, {l, 
                1}], 
FieldLine[{x, 
                exFL, -0.018405041298872132`}, {y, -eyFL, 0}, {l, 
                1}], 
FieldLine[{x, -exFL, -0.0746247850414778`}, {y, eyFL, 0}, {l, 
                1}], 
FieldLine[{x, 
                exFL, -0.0746247850414778`}, {y, -eyFL, 0}, {l, 
                1}], 
FieldLine[{x, -exFL, -0.11137468792739326`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.11137468792739326`}, {y, -eyFL, 0}, {l, 
                5}]}, 
{FieldLine[{x, -exFL, -0.47137001019010805`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, -0.544534304865613`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, -0.5750480021984988`}, {y, eyFL, 0}, {l, 
                35}], 
FieldLine[{x, -exFL, -0.5988278592923875`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, -exFL, -0.6192506111268778`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, -exFL, -0.6376220765775271`}, {y, eyFL, 0}, {l, 
                40}], 
FieldLine[{x, -exFL, -0.6546150340634312`}, {y, eyFL, 0}, {l, 45}], 
            FieldLine[{x, -exFL, -0.6706343665531647`}, {y, eyFL, 
                0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.6859504409773776`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.7007587894777939`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.7152107829127295`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, -exFL, -0.7294312458399684`}, {y, eyFL, 0}, {l, 
                80}]}, 
{FieldLine[{x, -exFL, -1.0023431869226649`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.0697486303716495`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.0982914518383011`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.1206749398534748`}, {y, eyFL, 0}, {l, 
                130}], 
FieldLine[{x, -exFL, -1.1399839040652335`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.1574137369258988`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, -exFL, -1.1735815891339774`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.188859690153044`}, {y, eyFL, 0}, {l, 
                170}], 
FieldLine[{x, -exFL, -1.2034972217257272`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, -exFL, -1.2176749065803385`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.231533098382144`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, -exFL, -1.2451879381196944`}, {y, eyFL, 0}, {l, 
                290}]}, 
{FieldLine[{x, -exFL, -1.512748607836687`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.5790439718379206`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.6071656881666812`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.629236457872938`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, -exFL, -1.6482869344969315`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.6654917015818393`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, -exFL, -1.6814572710151943`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, -exFL, -1.6965495313005405`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, -exFL, -1.711013480932306`}, {y, eyFL, 0}, {l, 
                410}], 
FieldLine[{x, -exFL, -1.7250268618252522`}, {y, eyFL, 0}, {l, 
                450}], 
FieldLine[{x, -exFL, -1.7387277595776625`}, {y, eyFL, 0}, {l, 
                520}], 
FieldLine[{x, -exFL, -1.7522304792498145`}, {y, eyFL, 0}, {l, 
                630}]}, 
{FieldLine[{x, -exFL, -2.017995148182311`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, -exFL, -2.111853202978992`}, {y, eyFL, 0}, {l, 
                480}], 
FieldLine[{x, -exFL, -2.1527553755376125`}, {y, eyFL, 0}, {l, 
                530}], 
FieldLine[{x, -exFL, -2.185757782086846`}, {y, eyFL, 0}, {l, 
                600}], 
FieldLine[{x, -exFL, -2.2151699988522813`}, {y, eyFL, 0}, {l, 
                
                710}], 
FieldLine[{x, -exFL, -2.2427532725714014`}, {y, eyFL, 0}, {l, 
                900}]}, 
{FieldLine[{x, -exFL, -2.6884676675144106`}, {y, eyFL, 0}, {l, 
                930}], 
FieldLine[{x, -exFL, -2.717807704673631`}, {y, eyFL, 0}, {l, 
                1100}], 
FieldLine[{x, -exFL, -2.7453246573357206`}, {y, eyFL, 0}, {l, 
                1390}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(3/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*3;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 2.6}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.029308421390798096`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.8018511678425502`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.27400881942977473`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.008898251473768173`, 
0.013301690167743248`, 
0.07634092102444598`, 
0.11993424867835069`, 
0.15135963333829838`, 
0.17748900915682148`, 
0.2006085876570872`, 
0.2218180787859236`}, 
{0.5407549053994128`, 
0.6123195357623479`, 
0.6423141353122429`, 
0.6657348975766476`, 
0.6858763318473625`, 
0.70401344360473`, 
0.7208036172188382`, 
0.7366427705400207`, 
0.7517954999107516`, 
0.766453336684262`, 
0.7807647015850679`, 
0.7948521161403765`}, 
{1.0666728632252338`, 
1.1338530436675336`, 
1.1623119206949895`, 
1.1846336121162426`, 
1.2038918453976428`, 
1.2212777636281922`, 
1.2374063498089172`, 
1.2526485447917701`, 
1.2672526829584667`, 
1.281398885742893`, 
1.2952270517225457`, 
1.3088529559752793`}, 
{1.5760857150724148`, 
1.6423098806184755`, 
1.6704038712675748`, 
1.6924537853346782`, 
1.711486848209975`, 
1.7286763223596944`, 
1.7446280420356792`, 
1.7597074902258532`, 
1.7741593965094276`, 
1.7881613098798226`, 
1.8018511678425502`, 
1.8153431542321279`}, 
{2.08097395939772`, 
2.1747882801035674`, 
2.2156729974364584`, 
2.2486618979976467`, 
2.278062445410946`, 
2.305635030701635`}, 
{2.58397147087727`, 
2.6775401141057933`, 
2.7183257399670473`, 
2.7512375434542147`, 
2.7805711719401764`, 
2.808082209985489`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*3;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*3;
eline1 = {{FieldLine[{x, exFL, 0.008923608406579086`}, {y, eyFL, 
                0}, {l, 5}], 
FieldLine[{x, exFL, 
                0.07634092102444598`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.07634092102444598`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.11993424867835069`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.11993424867835069`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.15135963333829838`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.15135963333829838`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.17748900915682148`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.17748900915682148`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.2006085876570872`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2006085876570872`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.2218180787859236`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2218180787859236`}, {y, -eyFL, 0}, {l, 
                5}]}, 
{FieldLine[{x, exFL, 
                0.5407549053994128`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.6123195357623479`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.6423141353122429`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.6657348975766476`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.6858763318473625`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, exFL, 
                0.70401344360473`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.7208036172188382`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.7366427705381801`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.7517954999107516`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, exFL, 
                0.766453336684262`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, exFL, 
                0.7807647015850679`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, exFL, 
                0.7948521161403765`}, {y, eyFL, 0}, {l, 
                100}]}, 
{FieldLine[{x, exFL, 
                1.0666728632252338`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.1338530436675336`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.1623119206949895`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.1846336121162426`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, exFL, 
                1.2038918453976428`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.2212777636281922`}, {y, eyFL, 0}, {l, 
                170}], 
FieldLine[{x, exFL, 
                1.2374063498089172`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.2526485447917701`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, exFL, 
                1.2672526829584667`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.281398885742893`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, exFL, 
                1.2952270517225457`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.3088529559752793`}, {y, eyFL, 0}, {l, 
                330}]}, 
{FieldLine[{x, exFL, 
                1.5760857150724148`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.6423098806184755`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.6704038712675748`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.6924537853346782`}, {y, eyFL, 0}, {l, 
                310}], 
FieldLine[{x, exFL, 
                1.711486848209975`}, {y, eyFL, 0}, {l, 
                330}], 
FieldLine[{x, exFL, 
                1.7286763223596944`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, exFL, 
                1.7446280420356792`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, exFL, 
                1.7597074902258532`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, exFL, 
                1.7741593965094276`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, exFL, 
                1.7881613098798226`}, {y, eyFL, 0}, {l, 
                490}], 
FieldLine[{x, exFL, 
                1.8018511678425502`}, {y, eyFL, 0}, {l, 
                560}], 
FieldLine[{x, exFL, 
                1.8153431542321279`}, {y, eyFL, 0}, {l, 
                680}]}, 
{FieldLine[{x, exFL, 
                2.08097395939772`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, exFL, 
                2.1747882801035674`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, exFL, 
                2.2156729974364584`}, {y, eyFL, 0}, {l, 
                560}], 
FieldLine[{x, exFL, 
                2.2486618979976467`}, {y, eyFL, 0}, {l, 
                640}], 
FieldLine[{x, exFL, 
                2.278062445410946`}, {y, eyFL, 0}, {l, 
                750}], 
FieldLine[{x, exFL, 
                2.305635030701635`}, {y, eyFL, 0}, {l, 
                960}]}, 
{FieldLine[{x, exFL, 
                2.7512375434542147`}, {y, eyFL, 0}, {l, 
                980}], 
FieldLine[{x, exFL, 
                2.7805711719401764`}, {y, eyFL, 0}, {l, 
                1150}], 
FieldLine[{x, exFL, 
                2.808082209985489`}, {y, eyFL, 0}, {l, 
                1460}]}};
eline2 = {{FieldLine[{x, -exFL, -0.008923608406579086`}, {y, 
                eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.07634092102444598`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.07634092102444598`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.11993424867835069`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.11993424867835069`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.15135963333829838`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.15135963333829838`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.17748900915682148`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.17748900915682148`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.2006085876570872`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2006085876570872`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.2218180787859236`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2218180787859236`}, {y, -eyFL, 0}, {l, 
                5}]}, 
{FieldLine[{x, -exFL, -0.5407549053994128`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.6123195357623479`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.6423141353122429`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.6657348975766476`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.6858763318473625`}, {y, eyFL, 0}, {l, 
                50}], 
FieldLine[{x, -exFL, -0.70401344360473`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.7208036172188382`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.7366427705381801`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.7517954999107516`}, {y, eyFL, 0}, {l, 
                
                65}], 
FieldLine[{x, -exFL, -0.766453336684262`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, -exFL, -0.7807647015850679`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, -exFL, -0.7948521161403765`}, {y, eyFL, 0}, {l, 
                100}]}, 
{FieldLine[{x, -exFL, -1.0666728632252338`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.1338530436675336`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.1623119206949895`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.1846336121162426`}, {y, eyFL, 0}, {l, 
                150}], 
FieldLine[{x, -exFL, -1.2038918453976428`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.2212777636281922`}, {y, eyFL, 0}, {l, 
                170}], 
FieldLine[{x, -exFL, -1.2374063498089172`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.2526485447917701`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, -exFL, -1.2672526829584667`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.281398885742893`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, -exFL, -1.2952270517225457`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.3088529559752793`}, {y, eyFL, 0}, {l, 
                330}]}, 
{FieldLine[{x, -exFL, -1.5760857150724148`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.6423098806184755`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.6704038712675748`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.6924537853346782`}, {y, eyFL, 0}, {l, 
                310}], 
FieldLine[{x, -exFL, -1.711486848209975`}, {y, eyFL, 0}, {l, 
                330}], 
FieldLine[{x, -exFL, -1.7286763223596944`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, -exFL, -1.7446280420356792`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, -exFL, -1.7597074902258532`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, -exFL, -1.7741593965094276`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, -exFL, -1.7881613098798226`}, {y, eyFL, 0}, {l, 
                490}], 
FieldLine[{x, -exFL, -1.8018511678425502`}, {y, eyFL, 0}, {l, 
                560}], 
FieldLine[{x, -exFL, -1.8153431542321279`}, {y, eyFL, 0}, {l, 
                680}]}, 
{FieldLine[{x, -exFL, -2.08097395939772`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, -exFL, -2.1747882801035674`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, -exFL, -2.2156729974364584`}, {y, eyFL, 0}, {l, 
                560}], 
FieldLine[{x, -exFL, -2.2486618979976467`}, {y, eyFL, 0}, {l, 
                640}], 
FieldLine[{x, -exFL, -2.278062445410946`}, {y, eyFL, 0}, {l, 
                750}], 
FieldLine[{x, -exFL, -2.305635030701635`}, {y, eyFL, 0}, {l, 
                960}]}, 
{FieldLine[{x, -exFL, -2.7512375434542147`}, {y, eyFL, 0}, {l, 
                980}], 
FieldLine[{x, -exFL, -2.7805711719401764`}, {y, eyFL, 0}, {l, 
                1150}], 
FieldLine[{x, -exFL, -2.808082209985489`}, {y, eyFL, 0}, {l, 
                1460}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(4/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*4;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 2.6}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.029308421390798096`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.8649334324332987`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.3538530638104737`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.012170480458297366`, 
0.08984449160515576`, 
0.1444560367434954`, 
0.17910434807252476`, 
0.20665962880231814`, 
0.23039687090897648`, 
0.2517421310843284`, 
0.27147199843852976`, 
0.2900706348463482`, 
0.3078710830472002`}, 
{0.6087566209101892`, 
0.6791751328200091`, 
0.7087856806028757`, 
0.731937111605014`, 
0.7518654273294991`, 
0.769823570126412`, 
0.7864578424909163`, 
0.8021576765754431`, 
0.8171834743270034`, 
0.8317238455228855`, 
0.8459250464268234`, 
0.8599079008107521`}, 
{1.1308012769537694`, 
1.1977917391142967`, 
1.2261793654059223`, 
1.2484484077921125`, 
1.2676632933152177`, 
1.285011595479559`, 
1.3011064745441163`, 
1.3163177865826428`, 
1.3308931516770328`, 
1.3450121835244666`, 
1.3588143955982481`, 
1.3724152525065485`}, 
{1.639359177790507`, 
1.7335891955967537`, 
1.7746379065385105`, 
1.8077529412520272`, 
1.8372619401642507`, 
1.8649334324332987`}, 
{2.1439249122563804`, 
2.2376991692690935`, 
2.2785678502009006`, 
2.311544323958408`, 
2.340934121164985`, 
2.3684968490099734`}, 
{2.646766636401121`, 
2.74031372831683`, 
2.781090569230355`, 
2.813995499281953`, 
2.843323133819512`, 
2.8708286356877957`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*4;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*4;
eline1 = {{FieldLine[{x, exFL, 0.012170480458297366`}, {y, eyFL, 
                0}, {l, 5}], 
FieldLine[{x, exFL, 
                0.08984449160515576`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.08984449160515576`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.1444560367434954`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.1444560367434954`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.17910434807252476`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.17910434807252476`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.20665962880231814`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.20665962880231814`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.23039687090897648`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.23039687090897648`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.2517421310843284`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2517421310843284`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.27147199843852976`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.27147199843852976`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.2900706348463482`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2900706348463482`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.3078710830472002`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.3078710830472002`}, {y, -eyFL, 0}, {l, 
                10}]}, 
{FieldLine[{x, exFL, 
                0.6087566209101892`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.6791751328200091`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.7087856806028757`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.731937111605014`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, exFL, 
                0.7518654273294991`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.769823570126412`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.7864578424909163`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, exFL, 
                0.8021576765754431`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, exFL, 
                0.8171834743270034`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, exFL, 
                0.8317238455228855`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, exFL, 
                0.8459250464268234`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, exFL, 
                0.8599079008107521`}, {y, eyFL, 0}, {l, 
                120}]}, 
{FieldLine[{x, exFL, 
                1.1308012769537694`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.1977917391142967`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.2261793654059223`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.2484484077921125`}, {y, eyFL, 0}, {l, 
                175}], 
FieldLine[{x, exFL, 
                1.2676632933152177`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.285011595479559`}, {y, eyFL, 0}, {l, 
                185}], 
FieldLine[{x, exFL, 
                1.3011064745441163`}, {y, eyFL, 0}, {l, 
                200}], 
FieldLine[{x, exFL, 
                1.3163177865826428`}, {y, eyFL, 0}, {l, 
                215}], 
FieldLine[{x, exFL, 
                1.3308931516770328`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, exFL, 
                1.3450121835244666`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, exFL, 
                1.3588143955982481`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, exFL, 
                1.3724152525065485`}, {y, eyFL, 0}, {l, 
                360}]}, 
{FieldLine[{x, exFL, 
                1.639359177790507`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, exFL, 
                1.7335891955967537`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, exFL, 
                1.7746379065385105`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, exFL, 
                1.8077529412520272`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, exFL, 
                1.8372619401642507`}, {y, eyFL, 0}, {l, 
                470}], 
FieldLine[{x, exFL, 
                1.8649334324332987`}, {y, eyFL, 0}, {l, 
                600}]}, 
{FieldLine[{x, exFL, 
                2.2376991692690935`}, {y, eyFL, 0}, {l, 
                540}], 
FieldLine[{x, exFL, 
                2.2785678502009006`}, {y, eyFL, 0}, {l, 
                600}], 
FieldLine[{x, exFL, 
                2.311544323958408`}, {y, eyFL, 0}, {l, 
                680}], 
FieldLine[{x, exFL, 
                2.340934121164985`}, {y, eyFL, 0}, {l, 
                800}], 
FieldLine[{x, exFL, 
                2.3684968490099734`}, {y, eyFL, 0}, {l, 
                1010}]}, 
{FieldLine[{x, exFL, 
                2.813995499281953`}, {y, eyFL, 0}, {l, 
                1020}], 
FieldLine[{x, exFL, 
                2.843323133819512`}, {y, eyFL, 0}, {l, 
                1210}], 
FieldLine[{x, exFL, 
                2.8708286356877957`}, {y, eyFL, 0}, {l, 
                1540}]}};
eline2 = {{FieldLine[{x, -exFL, -0.012170480458297366`}, {y, 
                eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.08984449160515576`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.08984449160515576`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.1444560367434954`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.1444560367434954`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.17910434807252476`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.17910434807252476`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.20665962880231814`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.20665962880231814`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.23039687090897648`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.23039687090897648`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.2517421310843284`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2517421310843284`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.27147199843852976`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.27147199843852976`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.2900706348463482`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2900706348463482`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.3078710830472002`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.3078710830472002`}, {y, -eyFL, 0}, {l, 
                10}]}, 
{FieldLine[{x, -exFL, -0.6087566209101892`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.6791751328200091`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.7087856806028757`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.731937111605014`}, {y, eyFL, 0}, {l, 
                55}], 
FieldLine[{x, -exFL, -0.7518654273294991`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.769823570126412`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.7864578424909163`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, -exFL, -0.8021576765754431`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, -exFL, -0.8171834743270034`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, -exFL, -0.8317238455228855`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, -exFL, -0.8459250464268234`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, -exFL, -0.8599079008107521`}, {y, eyFL, 0}, {l, 
                120}]}, 
{FieldLine[{x, -exFL, -1.1308012769537694`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.1977917391142967`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.2261793654059223`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.2484484077921125`}, {y, eyFL, 0}, {l, 
                175}], 
FieldLine[{x, -exFL, -1.2676632933152177`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.285011595479559`}, {y, eyFL, 0}, {l, 
                185}], 
FieldLine[{x, -exFL, -1.3011064745441163`}, {y, eyFL, 0}, {l, 
                200}], 
FieldLine[{x, -exFL, -1.3163177865826428`}, {y, eyFL, 0}, {l, 
                215}], 
FieldLine[{x, -exFL, -1.3308931516770328`}, {y, eyFL, 0}, {l, 
                230}], 
FieldLine[{x, -exFL, -1.3450121835244666`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, -exFL, -1.3588143955982481`}, {y, eyFL, 0}, {l, 
                300}], 
FieldLine[{x, -exFL, -1.3724152525065485`}, {y, eyFL, 0}, {l, 
                360}]}, 
{FieldLine[{x, -exFL, -1.639359177790507`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, -exFL, -1.7335891955967537`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, -exFL, -1.7746379065385105`}, {y, eyFL, 0}, {l, 
                350}], 
FieldLine[{x, -exFL, -1.8077529412520272`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, -exFL, -1.8372619401642507`}, {y, eyFL, 0}, {l, 
                470}], 
FieldLine[{x, -exFL, -1.8649334324332987`}, {y, eyFL, 0}, {l, 
                600}]}, 
{FieldLine[{x, -exFL, -2.2376991692690935`}, {y, eyFL, 0}, {l, 
                540}], 
FieldLine[{x, -exFL, -2.2785678502009006`}, {y, eyFL, 0}, {l, 
                600}], 
FieldLine[{x, -exFL, -2.311544323958408`}, {y, eyFL, 0}, {l, 
                680}], 
FieldLine[{x, -exFL, -2.340934121164985`}, {y, eyFL, 0}, {l, 
                800}], 
FieldLine[{x, -exFL, -2.3684968490099734`}, {y, eyFL, 0}, {l, 
                1010}]}, 
{FieldLine[{x, -exFL, -2.813995499281953`}, {y, eyFL, 0}, {l, 
                1020}], 
FieldLine[{x, -exFL, -2.843323133819512`}, {y, eyFL, 0}, {l, 
                1210}], 
FieldLine[{x, -exFL, -2.8708286356877957`}, {y, eyFL, 0}, {l, 
                1540}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(5/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*5;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 2.7}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.07903123056063544`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.4223087037436142`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.42820525565586964`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.01124061658563686`, 
0.04438119220029423`, 
0.18046399457326417`, 
0.22046155629776784`, 
0.25003954333375455`, 
0.2746934605787847`, 
0.29642508693462705`, 
0.31622886605048406`, 
0.33468702936600025`, 
0.3521796497803013`, 
0.36897632528294294`, 
0.3852823855583777`}, 
{0.6757564671789246`, 
0.7453242440018297`, 
0.7746424904546325`, 
0.7975866693300516`, 
0.817349645413207`, 
0.8351680205935128`, 
0.8516798571039623`, 
0.867269746228582`, 
0.882194947511441`, 
0.8966418734468045`, 
0.9107551457495939`, 
0.9246543004370051`}, 
{1.1947600850306417`, 
1.261589210611594`, 
1.2899158255361949`, 
1.3121396337411133`, 
1.3313171787924503`, 
1.3486330059587117`, 
1.3646987278361604`, 
1.3798832784943118`, 
1.394433670140297`, 
1.408529083700773`, 
1.4223087037436142`, 
1.4358877290442629`}, 
{1.702576010691596`, 
1.7967271529710591`, 
1.8377450582869186`, 
1.8708365210304556`, 
1.900325337609083`, 
1.9279784921339385`}, 
{2.206850374001075`, 
2.300587835718387`, 
2.3414417484077465`, 
2.374406761791941`, 
2.4037866331824893`, 
2.431340249915038`}, 
{2.7095482068713492`, 
2.8030751843902695`, 
2.8438438111907836`, 
2.8767423081686068`, 
2.90606432817138`, 
2.9335646404077527`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*5;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*5;
eline1 = {{FieldLine[{x, exFL, 0.01124061658563686`}, {y, eyFL, 
                0}, {l, 5}], 
FieldLine[{x, exFL, 
                0.18046399457326417`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.18046399457326417`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.22046155629776784`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.22046155629776784`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.25003954333375455`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.25003954333375455`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.2746934605787847`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2746934605787847`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.29642508693462705`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.29642508693462705`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.31622886605048406`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.31622886605048406`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.33468702936600025`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.33468702936600025`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.3521796497803013`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.3521796497803013`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.36897632528294294`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.36897632528294294`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.3852823855583777`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.3852823855583777`}, {y, -eyFL, 0}, {l, 
                10}]}, 
{FieldLine[{x, exFL, 
                0.6757564671789246`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.7453242440018297`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, exFL, 
                0.7746424904546325`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, exFL, 
                0.7975866693300516`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, exFL, 
                0.817349645413207`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, exFL, 
                0.8351680205935128`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, exFL, 
                0.8516798571039623`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, exFL, 
                0.867269746228582`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, exFL, 
                0.882194947511441`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.8966418734468045`}, {y, eyFL, 0}, {l, 
                105}], 
FieldLine[{x, exFL, 
                0.9107551457495939`}, {y, eyFL, 0}, {l, 
                120}], 
FieldLine[{x, exFL, 
                0.9246543004370051`}, {y, eyFL, 0}, {l, 
                145}]}, 
{FieldLine[{x, exFL, 
                1.1947600850306417`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.261589210611594`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.2899158255361949`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.3121396337411133`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, exFL, 
                1.3313171787924503`}, {y, eyFL, 0}, {l, 
                195}], 
FieldLine[{x, exFL, 
                1.3486330059587117`}, {y, eyFL, 0}, {l, 
                205}], 
FieldLine[{x, exFL, 
                1.3646987278361604`}, {y, eyFL, 0}, {l, 
                220}], 
FieldLine[{x, exFL, 
                1.3798832784943118`}, {y, eyFL, 0}, {l, 
                235}], 
FieldLine[{x, exFL, 
                1.394433670140297`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, exFL, 
                1.408529083700773`}, {y, eyFL, 0}, {l, 
                285}], 
FieldLine[{x, exFL, 
                1.4223087037436142`}, {y, eyFL, 0}, {l, 
                330}], 
FieldLine[{x, exFL, 
                1.4358877290442629`}, {y, eyFL, 0}, {l, 
                400}]}, 
{FieldLine[{x, exFL, 
                1.702576010691596`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, exFL, 
                1.7967271529710591`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, exFL, 
                1.8377450582869186`}, {y, eyFL, 0}, {l, 
                380}], 
FieldLine[{x, exFL, 
                1.8708365210304556`}, {y, eyFL, 0}, {l, 
                430}], 
FieldLine[{x, exFL, 
                1.900325337609083`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, exFL, 
                1.9279784921339385`}, {y, eyFL, 0}, {l, 
                650}]}, 
{FieldLine[{x, exFL, 
                2.3414417484077465`}, {y, eyFL, 0}, {l, 
                630}], 
FieldLine[{x, exFL, 
                2.374406761791941`}, {y, eyFL, 0}, {l, 
                720}], 
FieldLine[{x, exFL, 
                2.4037866331824893`}, {y, eyFL, 0}, {l, 
                840}], 
FieldLine[{x, exFL, 
                2.431340249915038`}, {y, eyFL, 0}, {l, 
                1070}]}, 
{FieldLine[{x, exFL, 
                2.90606432817138`}, {y, eyFL, 0}, {l, 
                1260}], 
FieldLine[{x, exFL, 
                2.9335646404077527`}, {y, eyFL, 0}, {l, 
                1610}]}};
eline2 = {{FieldLine[{x, -exFL, -0.01124061658563686`}, {y, 
                eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.18046399457326417`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.18046399457326417`}, {y, -eyFL, 0}, {l, 
                
                5}], 
FieldLine[{x, -exFL, -0.22046155629776784`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.22046155629776784`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.25003954333375455`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.25003954333375455`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.2746934605787847`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2746934605787847`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.29642508693462705`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.29642508693462705`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.31622886605048406`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.31622886605048406`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.33468702936600025`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.33468702936600025`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.3521796497803013`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.3521796497803013`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.36897632528294294`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.36897632528294294`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.3852823855583777`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.3852823855583777`}, {y, -eyFL, 0}, {l, 
                10}]}, 
{FieldLine[{x, -exFL, -0.6757564671789246`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.7453242440018297`}, {y, eyFL, 0}, {l, 
                60}], 
FieldLine[{x, -exFL, -0.7746424904546325`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, -exFL, -0.7975866693300516`}, {y, eyFL, 0}, {l, 
                65}], 
FieldLine[{x, -exFL, -0.817349645413207`}, {y, eyFL, 0}, {l, 
                70}], 
FieldLine[{x, -exFL, -0.8351680205935128`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, -exFL, -0.8516798571039623`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, -exFL, -0.867269746228582`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, -exFL, -0.882194947511441`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.8966418734468045`}, {y, eyFL, 0}, {l, 
                105}], 
FieldLine[{x, -exFL, -0.9107551457495939`}, {y, eyFL, 0}, {l, 
                120}], 
FieldLine[{x, -exFL, -0.9246543004370051`}, {y, eyFL, 0}, {l, 
                145}]}, 
{FieldLine[{x, -exFL, -1.1947600850306417`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.261589210611594`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.2899158255361949`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.3121396337411133`}, {y, eyFL, 0}, {l, 
                180}], 
FieldLine[{x, -exFL, -1.3313171787924503`}, {y, eyFL, 0}, {l, 
                195}], 
FieldLine[{x, -exFL, -1.3486330059587117`}, {y, eyFL, 0}, {l, 
                205}], 
FieldLine[{x, -exFL, -1.3646987278361604`}, {y, eyFL, 0}, {l, 
                220}], 
FieldLine[{x, -exFL, -1.3798832784943118`}, {y, eyFL, 0}, {l, 
                235}], 
FieldLine[{x, -exFL, -1.394433670140297`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, -exFL, -1.408529083700773`}, {y, eyFL, 0}, {l, 
                285}], 
FieldLine[{x, -exFL, -1.4223087037436142`}, {y, eyFL, 0}, {l, 
                330}], 
FieldLine[{x, -exFL, -1.4358877290442629`}, {y, eyFL, 0}, {l, 
                400}]}, 
{FieldLine[{x, -exFL, -1.702576010691596`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, -exFL, -1.7967271529710591`}, {y, eyFL, 0}, {l, 
                340}], 
FieldLine[{x, -exFL, -1.8377450582869186`}, {y, eyFL, 0}, {l, 
                380}], 
FieldLine[{x, -exFL, -1.8708365210304556`}, {y, eyFL, 0}, {l, 
                430}], 
FieldLine[{x, -exFL, -1.900325337609083`}, {y, eyFL, 0}, {l, 
                510}], 
FieldLine[{x, -exFL, -1.9279784921339385`}, {y, eyFL, 0}, {l, 
                650}]}, 
{FieldLine[{x, -exFL, -2.3414417484077465`}, {y, eyFL, 0}, {l, 
                630}], 
FieldLine[{x, -exFL, -2.374406761791941`}, {y, eyFL, 0}, {l, 
                720}], 
FieldLine[{x, -exFL, -2.4037866331824893`}, {y, eyFL, 0}, {l, 
                840}], 
FieldLine[{x, -exFL, -2.431340249915038`}, {y, eyFL, 0}, {l, 
                1070}]}, 
{FieldLine[{x, -exFL, -2.90606432817138`}, {y, eyFL, 0}, {l, 
                1260}], 
FieldLine[{x, -exFL, -2.9335646404077527`}, {y, eyFL, 0}, {l, 
                1610}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(6/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*6;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 2.7}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.020046579592771425`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.4857213647550453`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.4994193351481929`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.08675602559300638`, 
0.23568093078095972`, 
0.2794611447397052`, 
0.3096920869853872`, 
0.33436368575469105`, 
0.35589261372195885`, 
0.37539434201981847`, 
0.3934950926064519`, 
0.41059189317401545`, 
0.4269597178554959`, 
0.4428032827620889`, 
0.4582852641822243`}, 
{0.7420073084943407`, 
0.8109252788189985`, 
0.84001572616372`, 
0.8627969234209513`, 
0.8824289935827468`, 
0.9001360937929844`, 
0.9165499913838634`, 
0.9320515685767276`, 
0.9468956698388658`, 
0.9612670134118856`, 
0.975308956093118`, 
0.9891400333066778`}, 
{1.2585746066810162`, 
1.3252653425753131`, 
1.3535392998644744`, 
1.3757239495940832`, 
1.3948690931923806`, 
1.4121566842617344`, 
1.428197009832422`, 
1.4433582135567091`, 
1.4578867859236415`, 
1.4719615358805125`, 
1.4857213647550453`, 
1.4992812418502908`}, 
{1.7657422313451057`, 
1.859822498841804`, 
1.9008126052974532`, 
1.9338827507589982`, 
1.963353283459522`, 
1.9909897995758268`}, 
{2.269752450580996`, 
2.363456037167365`, 
2.4042963186586617`, 
2.4372507397501915`, 
2.466621426911204`, 
2.494166604771164`}, 
{2.7723171015858212`, 
2.865825275859458`, 
2.906586210641632`, 
2.939478677802695`, 
2.96879543106751`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*6;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*6;
eline1 = {{FieldLine[{x, exFL, 0.23568093078095972`}, {y, eyFL, 
                0}, {l, 10}], 
FieldLine[{x, exFL, 
                0.2794611447397052`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.2794611447397052`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.3096920869853872`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.3096920869853872`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.33436368575469105`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, 
                0.33436368575469105`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, exFL, 
                0.35589261372195885`}, {y, eyFL, 0}, {l, 
                7}], 
FieldLine[{x, -exFL, 
                0.35589261372195885`}, {y, -eyFL, 0}, {l, 
                7}], 
FieldLine[{x, exFL, 
                0.37539434201981847`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.37539434201981847`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.3934950926064519`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.3934950926064519`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.41059189317401545`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.41059189317401545`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.4269597178554959`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.4269597178554959`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.4428032827620889`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.4428032827620889`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.4582852641822243`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.4582852641822243`}, {y, -eyFL, 0}, {l, 
                15}]}, 
{FieldLine[{x, exFL, 
                0.7420073084943407`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, exFL, 
                0.8109252788189985`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, exFL, 
                0.84001572616372`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, exFL, 
                0.8627969234209513`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, exFL, 
                0.8824289935827468`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, exFL, 
                0.9001360937929844`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, exFL, 
                0.9165499913838634`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.9320515685767276`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, exFL, 
                0.9468956698388658`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, exFL, 
                0.9612670134118856`}, {y, eyFL, 0}, {l, 
                120}], 
FieldLine[{x, exFL, 
                0.975308956093118`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                0.9891400333066778`}, {y, eyFL, 0}, {l, 
                170}]}, 
{FieldLine[{x, exFL, 
                1.2585746066810162`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, exFL, 
                1.3252653425753131`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, exFL, 
                1.3535392998644744`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, exFL, 
                1.3757239495940832`}, {y, eyFL, 0}, {l, 
                200}], 
FieldLine[{x, exFL, 
                1.3948690931923806`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.4121566842617344`}, {y, eyFL, 0}, {l, 
                225}], 
FieldLine[{x, exFL, 
                1.428197009832422`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, exFL, 
                1.4433582135567091`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, exFL, 
                1.4578867859236415`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, exFL, 
                1.4719615358805125`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, exFL, 
                1.4857213647550453`}, {y, eyFL, 0}, {l, 
                360}], 
FieldLine[{x, exFL, 
                1.4992812418502908`}, {y, eyFL, 0}, {l, 
                440}]}, 
{FieldLine[{x, exFL, 
                1.7657422313451057`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, exFL, 
                1.859822498841804`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, exFL, 
                1.9008126052974532`}, {y, eyFL, 0}, {l, 
                410}], 
FieldLine[{x, exFL, 
                1.9338827507589982`}, {y, eyFL, 0}, {l, 
                460}], 
FieldLine[{x, exFL, 
                1.963353283459522`}, {y, eyFL, 0}, {l, 
                550}], 
FieldLine[{x, exFL, 
                1.9909897995758268`}, {y, eyFL, 0}, {l, 
                690}]}, 
{FieldLine[{x, exFL, 
                2.4042963186586617`}, {y, eyFL, 0}, {l, 
                670}], 
FieldLine[{x, exFL, 
                2.4372507397501915`}, {y, eyFL, 0}, {l, 
                760}], 
FieldLine[{x, exFL, 
                2.466621426911204`}, {y, eyFL, 0}, {l, 
                890}], 
FieldLine[{x, exFL, 
                2.494166604771164`}, {y, eyFL, 0}, {l, 
                1130}]}, 
{FieldLine[{x, exFL, 
                2.96879543106751`}, {y, eyFL, 0}, {l, 
                1320}]}};
eline2 = {{FieldLine[{x, -exFL, -0.23568093078095972`}, {y, 
                eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.2794611447397052`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.2794611447397052`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.3096920869853872`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.3096920869853872`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.33436368575469105`}, {y, eyFL, 0}, {l, 
                5}], 
FieldLine[{x, 
                exFL, -0.33436368575469105`}, {y, -eyFL, 0}, {l, 
                5}], 
FieldLine[{x, -exFL, -0.35589261372195885`}, {y, eyFL, 0}, {l, 
                7}], 
FieldLine[{x, 
                exFL, -0.35589261372195885`}, {y, -eyFL, 0}, {l, 
                7}], 
FieldLine[{x, -exFL, -0.37539434201981847`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.37539434201981847`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.3934950926064519`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.3934950926064519`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.41059189317401545`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.41059189317401545`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.4269597178554959`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.4269597178554959`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.4428032827620889`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.4428032827620889`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.4582852641822243`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.4582852641822243`}, {y, -eyFL, 0}, {l, 
                15}]}, 
{FieldLine[{x, -exFL, -0.7420073084943407`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, -exFL, -0.8109252788189985`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, -exFL, -0.84001572616372`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, -exFL, -0.8627969234209513`}, {y, eyFL, 0}, {l, 
                75}], 
FieldLine[{x, -exFL, -0.8824289935827468`}, {y, eyFL, 0}, {l, 
                80}], 
FieldLine[{x, -exFL, -0.9001360937929844`}, {y, eyFL, 0}, {l, 
                85}], 
FieldLine[{x, -exFL, -0.9165499913838634`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.9320515685767276`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, -exFL, -0.9468956698388658`}, {y, eyFL, 0}, {l, 
                110}], 
FieldLine[{x, -exFL, -0.9612670134118856`}, {y, eyFL, 0}, {l, 
                120}], 
FieldLine[{x, -exFL, -0.975308956093118`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -0.9891400333066778`}, {y, eyFL, 0}, {l, 
                170}]}, 
{FieldLine[{x, -exFL, -1.2585746066810162`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, -exFL, -1.3252653425753131`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, -exFL, -1.3535392998644744`}, {y, eyFL, 0}, {l, 
                190}], 
FieldLine[{x, -exFL, -1.3757239495940832`}, {y, eyFL, 0}, {l, 
                200}], 
FieldLine[{x, -exFL, -1.3948690931923806`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.4121566842617344`}, {y, eyFL, 0}, {l, 
                225}], 
FieldLine[{x, -exFL, -1.428197009832422`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, -exFL, -1.4433582135567091`}, {y, eyFL, 0}, {l, 
                260}], 
FieldLine[{x, -exFL, -1.4578867859236415`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, -exFL, -1.4719615358805125`}, {y, eyFL, 0}, {l, 
                320}], 
FieldLine[{x, -exFL, -1.4857213647550453`}, {y, eyFL, 0}, {l, 
                360}], 
FieldLine[{x, -exFL, -1.4992812418502908`}, {y, eyFL, 0}, {l, 
                440}]}, 
{FieldLine[{x, -exFL, -1.7657422313451057`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, -exFL, -1.859822498841804`}, {y, eyFL, 0}, {l, 
                370}], 
FieldLine[{x, -exFL, -1.9008126052974532`}, {y, eyFL, 0}, {l, 
                410}], 
FieldLine[{x, -exFL, -1.9338827507589982`}, {y, eyFL, 0}, {l, 
                460}], 
FieldLine[{x, -exFL, -1.963353283459522`}, {y, eyFL, 0}, {l, 
                550}], 
FieldLine[{x, -exFL, -1.9909897995758268`}, {y, eyFL, 0}, {l, 
                690}]}, 
{FieldLine[{x, -exFL, -2.4042963186586617`}, {y, eyFL, 0}, {l, 
                670}], 
FieldLine[{x, -exFL, -2.4372507397501915`}, {y, eyFL, 0}, {l, 
                760}], 
FieldLine[{x, -exFL, -2.466621426911204`}, {y, eyFL, 0}, {l, 
                890}], 
FieldLine[{x, -exFL, -2.494166604771164`}, {y, eyFL, 0}, {l, 
                1130}]}, 
{FieldLine[{x, -exFL, -2.96879543106751`}, {y, eyFL, 0}, {l, 
                1320}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

t=(7/8)T

等高線密度計算

ez2[
          x_] = eField[0, x, 0, 
              t][[3]]  /.   t -> ((π/(c*k0))/
                  8)*7;

    Plot[x*ez2[x], {x, 0, 
        3}, 
PlotRange -> {-0.08, 
          0.08}]

FindRoot[x*ez2[x] == 0, {x, 2.8}]

NMaximize[{x*ez2[x], 0 < x ≤ 0.1}, x]

流束(Flux)の計算

x0 = 1.4;
x1 = 1.5;
Ψs = simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Ψ0 = 0.0005;
Ψ1 = 0.0018533306427343426`;

x0 = 0.3256727988737908`;
x1 = 0.40476973065831984`;
simpi[x*Abs[ez2[x]], {x, x0, x1}, 10]

Clear[Ψ]

Ψ[x0_, x_] := 
        simpi[t*Abs[ez2[t]], {t, x0, x}, 10];
x0 = 0.24680871003882635`;
Plot[Ψ[x0, x], {x, x0, 
          2*x0}, 
PlotRange -> 
          All];
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 1.5490619974504123`;
FindRoot[Ψ[x0, x] == Ψ0, {x, 
        x0}]

x0 = 0.5686365892127628`;
FindRoot[Ψ[x0, x] == -Ψ1, {x, 
        x0}]

[等高線を描くためのx座標]

{{0.32588649245560447`, 
0.36161428813199226`, 
0.3883674740153332`, 
0.41089433824032956`, 
0.43090235440414615`, 
0.4492396331753508`, 
0.46640408023943536`, 
0.4827217195947351`, 
0.4984243045132127`, 
0.513688357592646`, 
0.5286571574306592`}, 
{0.8076832366414638`, 
0.8760930520041611`, 
0.9050023910985051`, 
0.9276530305619028`, 
0.9471796360043333`, 
0.9647966633785012`, 
0.9811309610568945`, 
0.9965605059197647`, 
1.01133824583326`, 
1.0256475647315126`, 
1.0396308199919897`, 
1.053405753498562`}, 
{1.3222653394022725`, 
1.3888364463210965`, 
1.4170646310755872`, 
1.4392151494917775`, 
1.458331990759753`, 
1.475594872873114`, 
1.4916129386196053`, 
1.5067536487843294`, 
1.5212630426479454`, 
1.53531960700679`, 
1.5490619974504123`, 
1.5626049837401643`}, 
{1.8288630317113386`, 
1.922879371827854`, 
1.963844304831666`, 
1.996895107189226`, 
2.026349021963882`, 
2.053970393749734`}, 
{2.3326330217937965`, 
2.426305350519396`, 
2.467133023319339`, 
2.5000776340947075`, 
2.5294398059901124`, 
2.5569771521343316`}, 
{2.835074158687742`, 
2.9285647286134893`, 
2.9693184498429637`, 
3.0022052571810685`, 
3.03151706312693`, 
3.05900792427791`}
}

[グラフィック]

<< ExtendGraphics`FieldLines`;
exFL = eField[0, x, y, t][[2]]  /.  
          t -> ((π/(c*k0))/
                  8)*7;
eyFL = eField[0, x, y, t][[3]]  /.  
          t -> ((π/(c*k0))/
                  8)*7;
eline1 = {{FieldLine[{x, exFL, 0.32588649245560447`}, {y, eyFL, 
                0}, {l, 15}], 
FieldLine[{x, exFL, 
                0.36161428813199226`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.3883674740153332`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, exFL, 
                0.41089433824032956`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.41089433824032956`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.43090235440414615`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.43090235440414615`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.4492396331753508`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.4492396331753508`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.46640408023943536`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, 
                0.46640408023943536`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, exFL, 
                0.4827217195947351`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.4827217195947351`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.4984243045132127`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.4984243045132127`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.513688357592646`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, 
                0.513688357592646`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, exFL, 
                0.5286571574306592`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, 
                0.5286571574306592`}, {y, -eyFL, 0}, {l, 
                20}]}, 
{FieldLine[{x, exFL, 
                0.8076832366414638`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.8760930520041611`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.9050023910985051`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.9276530305619028`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, exFL, 
                0.9471796360043333`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, exFL, 
                0.9647966633785012`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, exFL, 
                0.9811309610568945`}, {y, eyFL, 0}, {l, 
                105}], 
FieldLine[{x, exFL, 
                0.9965605059197647`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, exFL, 
                1.01133824583326`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, exFL, 
                1.0256475647315126`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, exFL, 
                1.0396308199919897`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, exFL, 
                1.053405753498562`}, {y, eyFL, 0}, {l, 
                195}]}, 
{FieldLine[{x, exFL, 
                1.3222653394022725`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.3888364463210965`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.4170646310755872`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, exFL, 
                1.4392151494917775`}, {y, eyFL, 0}, {l, 
                220}], 
FieldLine[{x, exFL, 
                1.458331990759753`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, exFL, 
                1.475594872873114`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, exFL, 
                1.4916129386196053`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, exFL, 
                1.5067536487843294`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, exFL, 
                1.5212630426479454`}, {y, eyFL, 0}, {l, 
                310}], 
FieldLine[{x, exFL, 
                1.53531960700679`}, {y, eyFL, 0}, {l, 
                345}], 
FieldLine[{x, exFL, 
                1.5490619974504123`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, exFL, 
                1.5626049837401643`}, {y, eyFL, 0}, {l, 
                485}]}, 
{FieldLine[{x, exFL, 
                1.8288630317113386`}, {y, eyFL, 0}, {l, 
                390}], 
FieldLine[{x, exFL, 
                1.922879371827854`}, {y, eyFL, 0}, {l, 
                390}], 
FieldLine[{x, exFL, 
                1.963844304831666`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, exFL, 
                1.996895107189226`}, {y, eyFL, 0}, {l, 
                500}], 
FieldLine[{x, exFL, 
                2.026349021963882`}, {y, eyFL, 0}, {l, 
                590}], 
FieldLine[{x, exFL, 
                2.053970393749734`}, {y, eyFL, 0}, {l, 
                740}]}, 
{FieldLine[{x, exFL, 
                2.467133023319339`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, exFL, 
                2.5000776340947075`}, {y, eyFL, 0}, {l, 
                800}], 
FieldLine[{x, exFL, 
                2.5294398059901124`}, {y, eyFL, 0}, {l, 
                940}], 
FieldLine[{x, exFL, 
                2.5569771521343316`}, {y, eyFL, 0}, {l, 
                1200}]}, 
{FieldLine[{x, exFL, 
                3.03151706312693`}, {y, eyFL, 0}, {l, 
                1380}], 
FieldLine[{x, exFL, 
                3.05900792427791`}, {y, eyFL, 0}, {l, 
                1760}]}};
eline2 = {{FieldLine[{x, -exFL, -0.32588649245560447`}, {y, 
                eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.36161428813199226`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.3883674740153332`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, -exFL, -0.41089433824032956`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.41089433824032956`}, {y, -eyFL, 0}, {l, 
                
                10}], 
FieldLine[{x, -exFL, -0.43090235440414615`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.43090235440414615`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.4492396331753508`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.4492396331753508`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.46640408023943536`}, {y, eyFL, 0}, {l, 
                10}], 
FieldLine[{x, 
                exFL, -0.46640408023943536`}, {y, -eyFL, 0}, {l, 
                10}], 
FieldLine[{x, -exFL, -0.4827217195947351`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.4827217195947351`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.4984243045132127`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.4984243045132127`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.513688357592646`}, {y, eyFL, 0}, {l, 
                15}], 
FieldLine[{x, 
                exFL, -0.513688357592646`}, {y, -eyFL, 0}, {l, 
                15}], 
FieldLine[{x, -exFL, -0.5286571574306592`}, {y, eyFL, 0}, {l, 
                20}], 
FieldLine[{x, 
                exFL, -0.5286571574306592`}, {y, -eyFL, 0}, {l, 
                20}]}, 
{FieldLine[{x, -exFL, -0.8076832366414638`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.8760930520041611`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.9050023910985051`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.9276530305619028`}, {y, eyFL, 0}, {l, 
                90}], 
FieldLine[{x, -exFL, -0.9471796360043333`}, {y, eyFL, 0}, {l, 
                95}], 
FieldLine[{x, -exFL, -0.9647966633785012`}, {y, eyFL, 0}, {l, 
                100}], 
FieldLine[{x, -exFL, -0.9811309610568945`}, {y, eyFL, 0}, {l, 
                105}], 
FieldLine[{x, -exFL, -0.9965605059197647`}, {y, eyFL, 0}, {l, 
                115}], 
FieldLine[{x, -exFL, -1.01133824583326`}, {y, eyFL, 0}, {l, 
                125}], 
FieldLine[{x, -exFL, -1.0256475647315126`}, {y, eyFL, 0}, {l, 
                140}], 
FieldLine[{x, -exFL, -1.0396308199919897`}, {y, eyFL, 0}, {l, 
                160}], 
FieldLine[{x, -exFL, -1.053405753498562`}, {y, eyFL, 0}, {l, 
                195}]}, 
{FieldLine[{x, -exFL, -1.3222653394022725`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.3888364463210965`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.4170646310755872`}, {y, eyFL, 0}, {l, 
                210}], 
FieldLine[{x, -exFL, -1.4392151494917775`}, {y, eyFL, 0}, {l, 
                220}], 
FieldLine[{x, -exFL, -1.458331990759753`}, {y, eyFL, 0}, {l, 
                240}], 
FieldLine[{x, -exFL, -1.475594872873114`}, {y, eyFL, 0}, {l, 
                250}], 
FieldLine[{x, -exFL, -1.4916129386196053`}, {y, eyFL, 0}, {l, 
                270}], 
FieldLine[{x, -exFL, -1.5067536487843294`}, {y, eyFL, 0}, {l, 
                290}], 
FieldLine[{x, -exFL, -1.5212630426479454`}, {y, eyFL, 0}, {l, 
                310}], 
FieldLine[{x, -exFL, -1.53531960700679`}, {y, eyFL, 0}, {l, 
                345}], 
FieldLine[{x, -exFL, -1.5490619974504123`}, {y, eyFL, 0}, {l, 
                400}], 
FieldLine[{x, -exFL, -1.5626049837401643`}, {y, eyFL, 0}, {l, 
                485}]}, 
{FieldLine[{x, -exFL, -1.8288630317113386`}, {y, eyFL, 0}, {l, 
                
                390}], 
FieldLine[{x, -exFL, -1.922879371827854`}, {y, eyFL, 0}, {l, 
                390}], 
FieldLine[{x, -exFL, -1.963844304831666`}, {y, eyFL, 0}, {l, 
                440}], 
FieldLine[{x, -exFL, -1.996895107189226`}, {y, eyFL, 0}, {l, 
                500}], 
FieldLine[{x, -exFL, -2.026349021963882`}, {y, eyFL, 0}, {l, 
                590}], 
FieldLine[{x, -exFL, -2.053970393749734`}, {y, eyFL, 0}, {l, 
                740}]}, 
{FieldLine[{x, -exFL, -2.467133023319339`}, {y, eyFL, 0}, {l, 
                700}], 
FieldLine[{x, -exFL, -2.5000776340947075`}, {y, eyFL, 0}, {l, 
                800}], 
FieldLine[{x, -exFL, -2.5294398059901124`}, {y, eyFL, 0}, {l, 
                940}], 
FieldLine[{x, -exFL, -2.5569771521343316`}, {y, eyFL, 0}, {l, 
                1200}]}, 
{FieldLine[{x, -exFL, -3.03151706312693`}, {y, eyFL, 0}, {l, 
                1380}], 
FieldLine[{x, -exFL, -3.05900792427791`}, {y, eyFL, 0}, {l, 
                1760}]}};
a = 0.01;
halfdip = {Line[{{a, -0.25}, {a, 0.25}, {-a, 
                0.25}, {-a, -0.25}, {a, -0.25}}]};
g = 
        Show[Graphics[{AbsoluteThickness[1], eline1, 
              eline2}], 
Prolog -> 
            halfdip, 
ImageSize -> {320, 
              320}, 
PlotRange -> {{-1, 
                1}, {-1, 1}}, 
AspectRatio -> 
            Automatic];

時間発展

z0 = 120. *π;
sol = 
      NDSolve[{R'[T] == 
            2*(z0*ethetaSumSpherical[R[T]/k0, θ[T], 0. , T/ω]*
                    hphiSumSpherical[R[T]/k0, θ[T], 0. , 
                      T/ω])/(ethetaSumSpherical[R[T]/k0, θ[T], 0. , T/ω]^2 + 
                    erSumSpherical[R[T]/k0, θ[T], 0. , T/ω]^2 + (((z0*hphiSumSpherical[R[T]/k0, θ[T], 0. , T/ω]))^2)), θ'[T] == -(2/(R[T]))*(z0*
                    erSumSpherical[R[T]/k0, θ[T], 0. , T/ω]*
                    hphiSumSpherical[R[T]/k0, θ[T], 0. , 
                      T/ω])/(ethetaSumSpherical[R[T]/k0, θ[T], 0. , T/ω]^2 + 
                    erSumSpherical[R[T]/k0, θ[T], 0. , T/ω]^2 + (((z0*hphiSumSpherical[R[T]/k0, θ[T], 0. , T/ω]))^2)), 
          R[0] == 
            k0*1.1065414794678605`, θ[0] == π/2}, {R[
            T], θ[T]}, {T, 0, ω}]

Plot[
        R[T]/k0  /.  sol[[1]], {T, 
          0, ω}, 
PlotRange -> 
          All];
Plot[θ[T]  /.  sol[[1]], {T, 
        0, ω}, 
PlotRange -> All]