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fennecslite/matlab/coaxialcloudfield.m
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coaxialcloudfield.m
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function [Phi,Er]=coaxialcloudfield(r,rm, rp, a, b, phia, phib,n,q)
% computes the potential and radial electric field inside an annular
% electron cloud confined in a coaxial geometry with bias phib-phia
% The cloud density is assumed uniform and the cloud is infinite in the
% axial direction
eps_0=8.85418781762E-12;
Phi=zeros(size(r));
Er=Phi;
%% Under the cloud
Phi(r>=a&r<=rm)=(phib-phia)/log(b/a)*log(r(r>=a&r<=rm)/a)+phia+...
log(r(r>=a&r<=rm)/a)/log(b/a)*(q*n/2/eps_0*(rp^2*log(b/rp)-rm^2*log(b/rm))...
+ q*n/4/eps_0*(rp^2-rm^2));
Er(r>=a&r<=rm)=-(phib-phia)/log(b/a)./r(r>=a&r<=rm)-...
1./r(r>=a&r<=rm)/log(b/a)*(q*n/2/eps_0*(rp^2*log(b/rp)-rm^2*log(b/rm))...
+ q*n/4/eps_0*(rp^2-rm^2));
%% In the cloud
Phi(r>rm&r<=rp)= (phib-phia)/log(b/a)*log(r(r>rm&r<=rp)/a)+phia -q*n/4/eps_0*r(r>rm&r<=rp).^2 +...
1/log(b/a)*(q*n/2/eps_0*(rp^2*log(b/rp)*log(r(r>rm&r<=rp)/a)-rm^2*log(a/rm)*log(r(r>rm&r<=rp)/b))...
+ q*n/4/eps_0*(rp^2*log(r(r>rm&r<=rp)/a)-rm^2*log(r(r>rm&r<=rp)/b)));
Er(r>rm&r<=rp)=-(phib-phia)./r(r>rm&r<=rp)/log(b/a) +q*n/2/eps_0*r(r>rm&r<=rp) -...
1/log(b/a)*(q*n/2/eps_0*(rp^2*log(b/rp)./r(r>rm&r<=rp)-rm^2*log(a/rm)./r(r>rm&r<=rp))...
+ q*n/4/eps_0*(rp^2./r(r>rm&r<=rp)-rm^2./r(r>rm&r<=rp)));
%% above the cloud
Phi(r>rp&r<=b)=(phib-phia)/log(b/a)*log(r(r>rp&r<=b)/a)+phia+...
log(b./r(r>rp&r<=b))/log(b/a)*(q*n/2/eps_0*(rp^2*log(rp/a)-rm^2*log(rm/a))...
- q*n/4/eps_0*(rp^2-rm^2));
Er(r>rp&r<=b)=-(phib-phia)/log(b/a)./r(r>rp&r<=b)+...
1./r(r>rp&r<=b)/log(b/a)*(q*n/2/eps_0*(rp^2*log(rp/a)-rm^2*log(rm/a))...
- q*n/4/eps_0*(rp^2-rm^2));
end
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