(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* Grisha Kirilin 2011 *)


BeginPackage["KIAS`KIASschool`" ]


movingCharge::usage="runs the manitulation dialog for moving cgarge electric field demonstration"
demonstration::usage="runs the manitulation dialog for n-prong antenna"
show3Dpattern::usage="auxilary function for the dialog for n-prong antenna"


Begin["`Private`"]


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vg==
"], {{0, 0}, {360., 358.56}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {360., 358.56}, PlotRange -> {{0, 360.}, {0, 358.56}}]};


demonstration[0]=Manipulate[rasterPlots[[\[Beta]]],{{\[Beta],1,"Speed of charge"},1,Length[\[Beta]List],1}];


pmax[\[Mu]_]=1/2 Sqrt[(1-9\[Mu]^2)(1-\[Mu]^2)];
pzmax[p_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},1/2 (p+\[Epsilon] Sqrt[1-(4\[Mu]^2)/(\[Epsilon]^2-p^2)])];
pzmin[p_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},1/2 (p-\[Epsilon] Sqrt[1-(4\[Mu]^2)/(\[Epsilon]^2-p^2)])];


kT[p_,pz_,\[Mu]_]=With[{\[Epsilon]=1-Sqrt[p^2+\[Mu]^2]},(1/4 (\[Epsilon]+(pz^2-(p-pz)^2)/\[Epsilon])^2-\[Mu]^2-pz^2)^(1/2)];


\[Epsilon][1,p_,pz_,\[Mu]_]=Sqrt[p^2+\[Mu]^2];
\[Epsilon][2,p_,pz_,\[Mu]_]=Sqrt[pz^2+kT[p,pz,\[Mu]]^2+\[Mu]^2];
\[Epsilon][3,p_,pz_,\[Mu]_]=Sqrt[(p-pz)^2+kT[p,pz,\[Mu]]^2+\[Mu]^2];


prongs[p_,pz_,\[Mu]_]={{-p,0},{pz,kT[p,pz,\[Mu]]},{p-pz,-kT[p,pz,\[Mu]]}};


prongs[\[Theta]_]={{1,0},RotationMatrix[\[Theta]].{1,0}};


singlePattern[q_,v_,n_]:=q Cross[v,n]/(1-v.n);


nProngPattern[vList_,eList_,n_]:=#.#&[Total[Table[singlePattern[eList[[i]],vList[[i]],n] ,{i,1,Length[vList]}]]];


TwoProng2D[{v_,\[Theta]_},\[Eta]_]=nProngPattern[{v{1,0,0},v Append[RotationMatrix[\[Theta]].{1,0},0]},{1,-1},{Cos[\[Eta]],Sin[\[Eta]],0}];


TwoProng3D[{v_,\[Theta]_},{\[Eta]_,\[Phi]_}]=nProngPattern[{v{1,0,0},v Append[RotationMatrix[\[Theta]].{1,0},0]},{1,-1},{Cos[\[Eta]],Sin[\[Eta]]Cos[\[Phi]],Sin[\[Eta]]Sin[\[Phi]]}];


ThreeProng2D[{p_,pz_,\[Mu]_},\[CapitalTheta]_]=nProngPattern[{{-p,0,0}/\[Epsilon][1,p,pz,\[Mu]],{pz,kT[p,pz,\[Mu]],0}/\[Epsilon][2,p,pz,\[Mu]],{p-pz,-kT[p,pz,\[Mu]],0}/\[Epsilon][3,p,pz,\[Mu]]},{1,-N[GoldenRatio],-1+N[GoldenRatio]},{Cos[\[Theta]],Sin[\[Theta]],0}];


ThreeProng3D[{p_,pz_,\[Mu]_},{\[CapitalTheta]_,\[Phi]_}]=nProngPattern[{{-p,0,0}/\[Epsilon][1,p,pz,\[Mu]],{pz,kT[p,pz,\[Mu]],0}/\[Epsilon][2,p,pz,\[Mu]],{p-pz,-kT[p,pz,\[Mu]],0}/\[Epsilon][3,p,pz,\[Mu]]},{1,-N[GoldenRatio],-1+N[GoldenRatio]},{Cos[\[Theta]],Sin[\[Theta]]Cos[\[Phi]],Sin[\[Theta]]Sin[\[Phi]]}];


prongStyle={Red,Blue,Darker[Green]};


pdemo[p_,\[Mu]_]=p pmax[\[Mu]];
pzdemo[p_,pz_,\[Mu]_]=pzmin[p pmax[\[Mu]],\[Mu]]+pz(pzmax[p pmax[\[Mu]],\[Mu]]-pzmin[p pmax[\[Mu]],\[Mu]]);


epilog[True,\[Theta]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
(* particle momenta *)
MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/2]}]}&,prongs[\[Theta]]],
(* paricles *)
MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/2],ImageScaled[0.01]]}&,prongs[\[Theta]]],
(* arc demonstration *)
{Gray,Line[{cPoint,ImageScaled[{1,.5}]}]},
{Gray,Circle[cPoint,ImageScaled[0.3],{0,\[Theta]}]},
(* point in the center *)
{Black,PointSize-> Medium,Point[{0,0}]}
}];


epilog[False,\[Theta]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
(* particle momenta *)
MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/2]}]}&,prongs[\[Theta]]],
(* paricles *)
MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/2],ImageScaled[0.01]]}&,prongs[\[Theta]]],
(* point in the center *)
{Black,PointSize-> Medium,Point[{0,0}]}
}];


epilog[True,p_,pz_,\[Mu]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
(* particle momenta *)
MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])]}]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
(* paricles *)
MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])],ImageScaled[0.01]]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
(* reference circle *)
{Gray,Circle[cPoint,ImageScaled[0.5]]},
(* pz projection line *)
{Dashed,Gray,Line[ImageScaled[{.5,.5}+#/(2pmax[\[Mu]])]&/@{{pzdemo[p,pz,\[Mu]],0},{pzdemo[p,pz,\[Mu]],kT[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]}}]},
{Gray,Line[ImageScaled[{.5,.5}+#/(2pmax[\[Mu]])]&/@{{pzdemo[p,pz,\[Mu]],0},{0,0}}]},
(* point in the center *)
{Black,PointSize-> Medium,Point[{0,0}]}
}];

epilog[False,p_,pz_,\[Mu]_]:=With[{cPoint=ImageScaled[{.5,.5}]},{
(* particle momenta *)
MapIndexed[{Opacity[.35],Thickness[0.015],prongStyle[[First@#2]],Line[{cPoint,ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])]}]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
(* paricles *)
MapIndexed[{prongStyle[[First@#2]],EdgeForm[Darker[prongStyle[[First@#2]]]],Disk[ImageScaled[{.5,.5}+#1/(2pmax[\[Mu]])],ImageScaled[0.01]]}&,prongs[pdemo[p,\[Mu]],pzdemo[p,pz,\[Mu]],\[Mu]]],
(* reference circle *)
{Gray,Circle[cPoint,ImageScaled[0.5]]},
(* point in the center *)
{Black,PointSize-> Medium,Point[{0,0}]}
}];


picture2prong2D[{True,showArc_},{\[Theta]_,v_}]:=PolarPlot[{TwoProng2D[{v,\[Theta]},\[Eta]]},{\[Eta],0,2\[Pi]},
PlotRange-> All,
Axes->False,
ImageSize->400,
PlotStyle->{Thickness[0.004],Black},
Epilog->epilog[showArc,\[Theta]]];

picture2prong2D[{False,showArc_},{\[Theta]_,v_}]:=Graphics[epilog[showArc,\[Theta]],ImageSize->400];


picture3prong2D[{True,showPZ_},p\[Beta]_,pz\[Beta]_,\[Mu]\[Beta]_]:=PolarPlot[{ThreeProng2D[{pdemo[p\[Beta],Exp[-\[Mu]\[Beta]]],pzdemo[p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]],Exp[-\[Mu]\[Beta]]},\[Theta]]},{\[Theta],0,2\[Pi]},
PlotRange-> All,
Axes->False,
ImageSize->400,
PlotStyle->{Thickness[0.004],Black},
Epilog->epilog[showPZ,p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]]];

picture3prong2D[{False,showPZ_},p\[Beta]_,pz\[Beta]_,\[Mu]\[Beta]_]:=Graphics[epilog[showPZ,p\[Beta],pz\[Beta],Exp[-\[Mu]\[Beta]]],ImageSize->400];


picture2prong3D[{{points3D_,mesh_},{\[Theta]_,v_}}]:=SphericalPlot3D[TwoProng3D[{v,\[Theta]},{\[Eta],\[Phi]}],{\[Eta],0,\[Pi]},{\[Phi],0,2\[Pi]},
PlotRange->All,
Axes->False,
Mesh-> mesh,
MeshStyle-> Directive[ColorData[6,"ColorList"][[6]] ,Opacity[0.3],Dashed],
Boxed->False,
PlotStyle->Directive[Green,Opacity[0.7]],
SphericalRegion->True,
ImageSize->300, 
PlotPoints->points3D]


picture3prong3D[{{points3D_,mesh_},{p\[Gamma]_,pz\[Gamma]_,\[Mu]\[Gamma]_}}]:=SphericalPlot3D[ThreeProng3D[{pdemo[p\[Gamma],Exp[-\[Mu]\[Gamma]]],pzdemo[p\[Gamma],pz\[Gamma],Exp[-\[Mu]\[Gamma]]],Exp[-\[Mu]\[Gamma]]},{\[Theta],\[Phi]}],{\[Theta],0,\[Pi]},{\[Phi],0,2\[Pi]},
PlotRange->All,
Axes->False,
Mesh-> mesh,
MeshStyle-> Directive[ColorData[6,"ColorList"][[6]] ,Opacity[0.3],Dashed],
Boxed->False,
PlotStyle->Directive[Green,Opacity[0.7]],
SphericalRegion->True,
ImageSize->300, 
PlotPoints->points3D]


show3Dpattern[flag_,obj_]:=If[flag,obj,Graphics3D[]];


\[Delta]=N[10^-8];

demonstration[1]=Module[{v\[Alpha]=Log[1-0.1],\[Theta]\[Alpha]=Log[N[\[Pi]/4]],showRP=False,showArc=False,show3D=False,mesh=5,box=False,points3D=10,object3D=Graphics3D[],arguments={{Automatic,5,True},{0.5,0.5,0.3}}},
Panel[
Grid[
{{"Log[1-v] ",Slider[Dynamic[v\[Alpha]],{Log[1-\[Delta]],Log[\[Delta]]}],"Show 2D pattern",Checkbox[Dynamic[showRP]],Row[{"Mesh:  ",Checkbox[Dynamic[mesh],{None,5}],"     Box:  ",Checkbox[Dynamic[box]]}],SpanFromLeft},
{"Log[\[Theta]] ",Slider[Dynamic[\[Theta]\[Alpha]],{Log[\[Delta]] ,Log[2\[Pi]-\[Delta]]}],"Show arc",Checkbox[Dynamic[showArc]],"3D quality:",RadioButtonBar[Dynamic[points3D],{10,30,50,70,100}]},
{" "," ","Show 3D pattern",Checkbox[Dynamic[show3D]],Button["Refresh 3D",showRP=False;object3D=picture2prong3D[{{points3D,mesh},{Exp[\[Theta]\[Alpha]],1-Exp[v\[Alpha]]}}];showRP=True;,ImageSize->Medium,Method->"Queued"]," "},
{Dynamic[picture2prong2D[{showRP,showArc},{Exp[\[Theta]\[Alpha]],1-Exp[v\[Alpha]]}]],SpanFromLeft,SpanFromLeft,SpanFromLeft,Dynamic[Show[show3Dpattern[show3D,object3D],Boxed->box]],SpanFromLeft}},
Alignment->Left,
Frame->{None,None,{{{1,3},{1,2}}->True,{{1,3},{3,4}}->True,{{4,4},{1,4}}->True,{{1,3},{5,6}}->True,{{5,4},{5,6}}->box}},
FrameStyle->LightGray,
Spacings->{{1,1,3,1,3,1,1},{1,1,1,3,1}}]
]];


\[Delta]=N[10^-5];

demonstration[2]=Module[{p\[Alpha]=0.5,pz\[Alpha]=0.5,\[Mu]\[Alpha]=-Log[0.3],showRP=False,showPZ=False,show3D=False,mesh=5,box=False,points3D=10,object3D=Graphics3D[],arguments={{Automatic,5,True},{0.5,0.5,0.3}}},
Panel[
Grid[
{{"ln\!\(\*FractionBox[\(Q\), \(m\)]\) ",Slider[Dynamic[\[Mu]\[Alpha]],{-Log[\[Delta]],-Log[1/3-\[Delta]]}],"Show 2D pattern",Checkbox[Dynamic[showRP]],Row[{"Mesh:  ",Checkbox[Dynamic[mesh],{None,5}],"     Box:  ",Checkbox[Dynamic[box]]}],SpanFromLeft},
{"p ",Slider[Dynamic[p\[Alpha]],{\[Delta] 10^-3,1-\[Delta]}],"Show \!\(\*SubscriptBox[\(p\), \(z\)]\) projection",Checkbox[Dynamic[showPZ]],"3D quality:",RadioButtonBar[Dynamic[points3D],{10,30,50,70,100}]},
{"\!\(\*SubscriptBox[\(p\), \(z\)]\) ",Slider[Dynamic[pz\[Alpha]],{\[Delta] 10^-3,1-\[Delta] 10^-3}],"Show 3D pattern",Checkbox[Dynamic[show3D]],Button["Refresh 3D",showRP=False;object3D=picture3prong3D[{{points3D,mesh},{p\[Alpha],pz\[Alpha],\[Mu]\[Alpha]}}];showRP=True;,ImageSize->Medium,Method->"Queued"]," "},
{Dynamic[picture3prong2D[{showRP,showPZ},p\[Alpha],pz\[Alpha],\[Mu]\[Alpha]]],SpanFromLeft,SpanFromLeft,SpanFromLeft,Dynamic[Show[show3Dpattern[show3D,object3D],Boxed->box]],SpanFromLeft}},
Alignment->Left,
Frame->{None,None,{{{1,3},{1,2}}->True,{{1,3},{3,4}}->True,{{4,4},{1,4}}->True,{{1,3},{5,6}}->True,{{5,4},{5,6}}->box}},
FrameStyle->LightGray,
Spacings->{{1,1,3,1,3,1,1},{1,1,1,3,1}}]
]];


\[Delta]2=\[Pi] 10^-5;
doublePattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.np+\[Delta]2^2)(1-n.nm)+\[Delta]2^2)];
plusPattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.np+\[Delta]2^2)(2-n.(nm+np)+\[Delta]2^2))];
minusPattern[\[Phi]_,\[Chi]_]=With[{n={Cos[\[Chi]],Sin[\[Chi]],0},np={1,0,0},nm={Cos[\[Phi]],Sin[\[Phi]],0}},(2(1-nm.np))/((1-n.nm+\[Delta]2^2)(2-n.(nm+np)+\[Delta]2^2))];


doubleZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],doublePattern[\[Phi],\[Chi]]];
plusZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],plusPattern[\[Phi],\[Chi]]];
minusZoom[{\[Phi]_,\[Chi]_},rmax_]:=If[#2>rmax #1,rmax #1,#2]&[doublePattern[\[Phi],\[Phi]/2],minusPattern[\[Phi],\[Chi]]];


cP={0.0,0.0};
vectors[\[Phi]_,r_]:={
{PointSize->Large,Point[cP]},
{PointSize->Large,Red,Point[r{1,0}]},
{PointSize->Large,Blue,Point[r RotationMatrix[{{Cos[\[Phi]],-Sin[\[Phi]]},{1,0}}].{1,0}]},
{Opacity[.35],Thickness[0.0125],Red,Line[{cP,cP+r{1,0}}]},
{Opacity[.35],Thickness[0.0125],Blue,Line[{cP,cP+r RotationMatrix[{{Cos[\[Phi]],-Sin[\[Phi]]},{1,0}}].{1,0}}]}}


polar[\[Phi]_,rmax_]:=PolarPlot[
{rmax doublePattern[\[Phi],\[Phi]/2],doubleZoom[{\[Phi],\[Chi]},rmax],plusZoom[{\[Phi],\[Chi]},rmax],minusZoom[{\[Phi],\[Chi]},rmax]},{\[Chi],0,2Pi},
Frame->True,
PlotRange->1.1rmax doublePattern[\[Phi],\[Phi]/2]{{-1,1},{-1,1}},
Epilog->vectors[\[Phi],1.1rmax doublePattern[\[Phi],\[Phi]/2]],
PlotPoints->50,
Axes->False,
ImageSize->500];


demonstration[3]=Manipulate[polar[\[Theta],rmax],{{\[Theta],\[Pi]/4,"\[Theta]"},\[Delta]2,\[Pi]-\[Delta]2},{{rmax,10,"Zoom out"},0.1,20}];


End[]


EndPackage[]
