File:Bremsstrahlung.gif

Bremsstrahlung.gif (360 × 240 pixels, file size: 3.29 MB, MIME type: image/gif, looped, 81 frames)

Summary

Description
English: Field lines and modulus of the electric field generated by a (negative) charge first moving at constant speed and then stopping quickly (not instantaneously, but quickly) to show the generated bremsstrahlung radiation.
Date
Source https://twitter.com/j_bertolotti/status/1056921689643249666
Author Jacopo Bertolotti
Permission
(Reusing this file)
https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

rs[t_] := {-(E^(-2500 t^2)/(150 Sqrt[\[Pi]])) + t/3 - 1/3 t Erf[50 t],
    0, 0};
c = 1;
q = -1;
\[Beta][t_] := {(1 - Erf[50 t])/3, 0, 0};
d\[Beta][t_] := Chop@Evaluate@D[\[Beta][t1], t1] /. t1 -> t;

Plot[(\[Beta][t])[[1]], {t, -0.1, 0.1}, PlotRange -> All]
Plot[(d\[Beta][t])[[1]], {t, -0.1, 0.1}, PlotRange -> All]
\[Gamma][t_] := 1/Sqrt[1 - Norm[\[Beta][t]]^2];
n[r_, t_] := (r - rs[t])/Norm[r - rs[t]];
tr[r_, t_] := t - Norm[r - rs[t]]/c;
Ef[r_, t_] := (q (n[r, t] - \[Beta][t])/(\[Gamma][
      t]^2 (1 - n[r, t].\[Beta][t])^3 Norm[r - rs[t]]^2) + 
   q n[r, t] \[Cross]((n[r, t] - \[Beta][t])\[Cross]d\[Beta][t])/(
    c (1 - n[r, t].\[Beta][t])^3 Norm[r - rs[t]]) )
\[Tau] = 0.75;
StreamPlot[
 Ef[{x, y, 0}, tr[{x, y, 0}, \[Tau]]][[1 ;; 2]], {x, -1, 1}, {y, -1, 
  1}, VectorPoints -> 20]
Bf[r_, t_] := (q (
    c (\[Beta][t]\[Cross]n[r, t]))/(\[Gamma][
      t]^2 (1 - n[r, t].\[Beta][t])^3 Norm[r - rs[t]]^2) + 
   q n[r, t] \[Cross](n[r, 
        t]\[Cross]((n[r, t] - \[Beta][t])\[Cross]d\[Beta][t]))/((1 - 
       n[r, t].\[Beta][t])^3 Norm[r - rs[t]]) )
S[r_, t_] := Ef[r, t]\[Cross]Bf[r, t]

p1 = Table[
   StreamDensityPlot[{Ef[{x, y, 0}, tr[{x, y, 0}, \[Tau]]][[1 ;; 2]], 
     Log@Norm@Ef[{x, y, 0}, tr[{x, y, 0}, \[Tau]]][[1 ;; 2]]}, {x, -2,
      1}, {y, -1, 1}, ColorFunction -> "SunsetColors", 
    StreamPoints -> Medium, StreamStyle -> {White}, PlotRange -> All, 
    Frame -> False, MaxRecursion -> 5, AspectRatio -> 2/3]
   , {\[Tau], -2.5, 1.5, 0.05}];

ListAnimate[p1]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

This file, which was originally posted to https://twitter.com/j_bertolotti/status/1056921689643249666, was reviewed on 30 October 2018 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.

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