eicoll_dke_yp

Electron-ion collision operator (non-relativistic limit)

By Joan Decker (MIT-RLE) and Yves Peysson (CEA-DRFC,yves.peysson@cea.fr)

0001 function [Fei,Aei,Btei] = eicoll_dke_yp(v,zZi,zmi,xzni_norm,xzTi_norm,ir,coll_mode)
0002 %
0003 %Electron-ion collision operator (non-relativistic limit)
0004 %
0005 %By Joan Decker (MIT-RLE) and Yves Peysson (CEA-DRFC,yves.peysson@cea.fr)
0006 %
0007 if nargin < 7,
0008     error('Wrong number of input arguments in eicoll_dke_yp')
0009 end
0010 %
0011 me = 1/1860;%Electron rest mass (u.m.a. units)
0012 v2 = v.*v;
0013 %
0014 if coll_mode == 1,%High-velocity limit
0015     Fei = sum(zZi.^2.*(me./zmi).*xzni_norm(:,ir)')./v2;
0016     Aei = sum(zZi.^2.*(me./zmi).*xzni_norm(:,ir)'.*xzTi_norm(:,ir)')./v./v2;
0017     Btei = sum(zZi.^2.*xzni_norm(:,ir)')./v/2 - sum(zZi.^2.*xzni_norm(:,ir)'.*(me./zmi).*xzTi_norm(:,ir)')./v./v2/2;
0018 elseif coll_mode == 3,%Lorentz model
0019     Fei = zeros(size(v));
0020     Aei = zeros(size(v));
0021     Btei = ones(size(v))/2;
0022 elseif coll_mode == 5,%Ultrarelativistic Moller model
0023    Fei = zeros(size(v));
0024    Aei = zeros(size(v));
0025    Btei = sum(((zZi'.^2.*xzni_norm(:,ir))*ones(1,length(v))))./v/2;
0026 else,%Maxwellian background (non-relativistic limit)
0027     xzTi_norm(find(xzTi_norm(:,ir)==0),ir) = eps;%To remove singularities when Ti = 0 exactly
0028     u = (ones(size(xzTi_norm(:,ir)))*v)./(sqrt(xzTi_norm(:,ir).*(me./zmi'))*ones(1,length(v)))./sqrt(2);
0029 %
0030     Fei = sum(((zZi'.^2.*(me./zmi').*xzni_norm(:,ir))*ones(1,length(v))).*(erf(u)-2*u.*exp(-u.^2)/sqrt(pi)))./v2;
0031     Aei = sum(((zZi'.^2.*xzni_norm(:,ir))*ones(1,length(v))).*(erf(u)-2*u.*exp(-u.^2)/sqrt(pi))./u./u)./v/2;    
0032     Btei = sum(((zZi'.^2.*xzni_norm(:,ir))*ones(1,length(v))).*((2-1./u./u).*erf(u) + 2*exp(-u.^2)./u/sqrt(pi)))./v/4;
0033 end