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Simplified radiation integrals in wigglers (#188)
* Wiggler field, wiggler integrals * Correct global variable name (#187) * corrected Bwig * Bug fixes * Bug fixes * Bug fixes * Updated atsummary and removed debug info * Analytical I3 * amat, atradon * Fixed missing 'beta' in sync tune and bunch length * Fixed missing 'beta' in sync tune and bunch length * Removed temp files * Fix import of wigglers from matlab * Check overvoltage < 1 * Wiggler radiation in python * Remove useless import, bug fix * Improved docstring * vector ordering in amat * fix coupled tunes * Handle wigglers in atradon and atradoff * Ignore wigglers using DriftPass Co-authored-by: Laurent Farvacque <laurent.farvacque@gmail.com>
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,114 @@ | ||
| function [I1,I2,I3,I4,I5] = WigglerRadiation(ring,lindata) | ||
| %WIGGLERRADIATION Compute the radiation integrals in wigglers | ||
| % | ||
| %[I1,I2,I3,I4,I5] = WIGGLERRADIATION(RING,LINDATA) | ||
| % | ||
| %RING Lattice structure | ||
| %LINDATA Output of atlinopt for all lattice elements | ||
| % | ||
| %WigglerRadiation computes the radiation integrals for all wigglers with | ||
| %the following approximations: | ||
| % | ||
| %- The self-induced dispersion is neglected in I4 and I5, but is is used as | ||
| % a lower limit for the I5 contribution | ||
| % | ||
| % I1, I2 are integrated analytically | ||
| % I3 is integrated analytically for a single harmonic, numerically otherwise | ||
|
|
||
| nstep=60; | ||
| e_mass=PhysConstant.electron_mass_energy_equivalent_in_MeV.value*1e6; % eV | ||
| cspeed = PhysConstant.speed_of_light_in_vacuum.value; % m/s | ||
|
|
||
| iswiggler=@(elem) strcmp(elem.Class,'Wiggler') && ~strcmp(elem.PassMethod,'DriftPass'); | ||
| wigglers=cellfun(iswiggler, ring); | ||
| if any(wigglers) | ||
| energy=unique(atgetfieldvalues(ring(wigglers),'Energy')); | ||
| if length(energy) > 1 | ||
| error('AT:NoEnergy','Energy field not equal for all elements'); | ||
| end | ||
| Brho=sqrt(energy*energy - e_mass*e_mass)/cspeed; | ||
| vini=lindata([wigglers;false])'; | ||
| [di1,di2,di3,di4,di5]=cellfun(@wigrad,ring(wigglers),num2cell(vini)); | ||
| I1=sum(di1); | ||
| I2=sum(di2); | ||
| I3=sum(di3); | ||
| I4=sum(di4); | ||
| I5=sum(di5); | ||
| else | ||
| [I1,I2,I3,I4,I5]=deal(0); | ||
| end | ||
|
|
||
| function [di1,di2,di3,di4,di5]=wigrad(elem,dini) | ||
| le=elem.Length; | ||
| alphax0=dini.alpha(1); | ||
| betax0=dini.beta(1); | ||
| gammax0=(alphax0.*alphax0+1)./betax0; | ||
| eta0 = dini.Dispersion(1); | ||
| etap0 = dini.Dispersion(2); | ||
| H0=gammax0*eta0*eta0 + 2*alphax0*eta0*etap0 + betax0*etap0*etap0; | ||
| avebetax=betax0+alphax0*le+gammax0*le*le/3; | ||
|
|
||
| kw=2*pi/elem.Lw; | ||
| rhoinv=elem.Bmax/Brho; | ||
| coefh=elem.By(2,:)*rhoinv; | ||
| coefv=elem.Bx(2,:)*rhoinv; | ||
| coef2=[coefh coefv]; | ||
| if length(coef2)==1 % Analytical I3 | ||
| di3=coef2^3*4*le/3/pi; | ||
| else % Numerical I3 | ||
| [bx,bz]=Baxis(elem,linspace(0,elem.Lw,nstep+1)); | ||
| B2=bx.*bx+bz.*bz; | ||
| rinv=sqrt(B2)/Brho; | ||
| di3=trapz(rinv.^3)*le/nstep; | ||
| end | ||
| di2=elem.Length*(coefh*coefh'+coefv*coefv')/2; | ||
| di1=-di2/kw/kw; | ||
| di4=0; | ||
| if ~isempty(coefh) | ||
| d5lim=4*avebetax*le*coefh(1)^5/15/pi/kw/kw; | ||
| else | ||
| d5lim = 0; | ||
| end | ||
| di5=max(H0*di3,d5lim); | ||
| % fprintf('%s\t%e\t%e\t%e\t%e\t%e\t(%e,%e,%e)\n',elem.FamName,di1,di2,di3,di4,di5,d5lim,H0*di3,dini.Dispersion(1)); | ||
| % avebetaz=dini.beta(2)+dini.alpha(2)*le+(1+dini.alpha(2)^2)/dini.beta(2)*le*le/3; | ||
| % dnuz=avebetaz*di2/8/pi; | ||
| % fprintf('%s\t%e\t%e\n',elem.FamName,dnuz,avebetaz) | ||
| end | ||
|
|
||
| function [bx,bz] = Baxis(wig,s) | ||
| %Bwig Compute the field on the axis of a generic wiggler | ||
| % | ||
| %The field of an horizontal wiggler is represented by a sum of harmonics, | ||
| %each being described by a 6x1 column in a matrix By such as: | ||
| % | ||
| % Bz/Bmax = -By2 * cos(By5*kw*s + By6) | ||
| % | ||
| %The field of an vertical wiggler is represented by a sum of harmonics, | ||
| %each being described by a 6x1 column in a matrix Bx such as: | ||
| % | ||
| % Bx/Bmax = Bx2 * cos(Bx5*kw*s + Bx6) | ||
|
|
||
| kw=2*pi/wig.Lw; | ||
| Bmax=wig.Bmax; | ||
| kws=kw*s; | ||
| [bxh,bzh]=cellfun(@harmh,num2cell(wig.By,1),'UniformOutput',false); | ||
| [bxv,bzv]=cellfun(@harmv,num2cell(wig.Bx,1),'UniformOutput',false); | ||
| bx=sum(cat(3,bxh{:},bxv{:}),3); | ||
| bz=sum(cat(3,bzh{:},bzv{:}),3); | ||
|
|
||
| function [bx,bz]=harm(pb) | ||
| bz=-Bmax*pb(2)*cos(pb(5)*kws+pb(6)); | ||
| bx=zeros(size(kws)); | ||
| end | ||
| function [bx,bz]=harmh(pb) | ||
| [bx,bz]=harm(pb); | ||
| end | ||
| function [bx,bz]=harmv(pb) | ||
| [bz,fz]=harm(pb); | ||
| bx=-fz; | ||
| end | ||
| end | ||
|
|
||
| end | ||
|
|
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