Analytic_stpe_dens_Efield.m
dcbebf0c577cmaster

Analytic_stpe_dens_Efield.m
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			function [Phi,Er] = Analytic_stpe_dens_Efield(a,b,deltaphi,rm,rp,n,r)
			%Analytic_stpe_dens_Efield Computes the electric field and potential for a
			% step density in a biased coaxial geometry
			%

			q=1.602176620000000e-19;
			eps0=8.854187817620000e-12;
			phia=-deltaphi;
			phib=0;


			phip=1/log(b/a)(qn/2/eps0rm^2log(b/rp)log(rp/rm)+(phia + qn/2/eps0(rp^2-rm^2)(log(rp/a)-0.5))*log(b/rp));
			phim=1/log(b/a)(-qn/2/eps0rm^2log(rm/a)log(rp/rm)+( qn/2/eps0(rp^2-rm^2)(log(b/rp)+0.5))log(rm/a)+phialog(b/rm));

			Phi=zeros(size(r));
			Er=zeros(size(r));

			Phi(r>=a & r<rm)=((phim-phia)log(r(r>=a & r<rm))+phialog(rm)-phim*log(a))/log(rm/a);
			Phi(r>=rm & r<rp)=-qn/4/eps0(r(r>=rm & r<rp).^2-rp^2) ...
			+(phip-phim +qn/4/eps0(rp^2-rm^2))/log(rp/rm)*log(r(r>=rm & r<rp)/rp)...
			+phip;
			Phi(r>=rp & r<=b)=((phib-phip)log(r(r>=rp & r<=b))+phiplog(b)-phib*log(rp))/log(b/rp);

			Er(r>=a & r<rm)=-(phim-phia)./r(r>=a & r<rm)/log(rm/a);
			Er(r>=rm & r<rp)=+qn/2/eps0r(r>=rm & r<rp) ...
			-(phip-phim +qn/4/eps0(rp^2-rm^2))/log(rp/rm)./r(r>=rm & r<rp);
			Er(r>=rp & r<=b)=-(phib-phip)./r(r>=rp & r<=b)/log(b/rp);

			end