VacLifetimeResidualGass

 Coloumb scattering and residual gas Bremsstrahlung Cross sections are
 computed to evaluate the lifetime contribution of the vacuum system
 specified by Zperc (vector of percentages, index=atomic Number),and P[nTor] the
 pressure profile along the ring
 b is the dimension of the vacuum chamber along the lattice (x,y).
 DEE is the Energy acceptance of the ring (longitudinal aperture)

 length(b)=length(DEE)=length(P)=length(ring)

 Assumed temperature of 293 K and interacion with diatomic gas
 
 tvac returned in hours
 
 created 20-5-2013

0001 function [tvac,sigmacoulomb,sigmabremsstrahlung]=...
0002     VacLifetimeResidualGass(ring,DEE,Zperc,P,b)
0003 % Coloumb scattering and residual gas Bremsstrahlung Cross sections are
0004 % computed to evaluate the lifetime contribution of the vacuum system
0005 % specified by Zperc (vector of percentages, index=atomic Number),and P[nTor] the
0006 % pressure profile along the ring
0007 % b is the dimension of the vacuum chamber along the lattice (x,y).
0008 % DEE is the Energy acceptance of the ring (longitudinal aperture)
0009 %
0010 % length(b)=length(DEE)=length(P)=length(ring)
0011 %
0012 % Assumed temperature of 293 K and interacion with diatomic gas
0013 %
0014 % tvac returned in hours
0015 %
0016 % created 20-5-2013
0017 
0018 r0=2.8179403267e-15;%[m] classical electron radius
0019 c=299792458;% m/s speed of ligth
0020 me=0.510998910e6;% eV/c^2 electron mass
0021 alpha=1/137.035999084; % fine structure constant
0022 kboltz=1.3806488e-23 ; %m^2 kg s^-2 K^-1 Boltzman constant
0023 T=293;%K
0024 
0025 % particle energy
0026 E0=ring{1}.Energy;% eV/c electron beam energy
0027 
0028 l=atlinopt(ring,0,1:length(ring));
0029 betx=arrayfun(@(x)x.beta(1),l)';
0030 bety=arrayfun(@(x)x.beta(2),l)';
0031 
0032 Z=1:length(Zperc);
0033 
0034 sgcv=max(bety).*bety./b(:,2).^2;
0035 
0036 sgch=max(betx).*betx./b(:,1).^2;
0037 
0038 % test parameters, with this it should return 0.13 barn
0039 % sgch=0;
0040 % sgcv=30*15/0.03^2;
0041 % E0=5e9;
0042 
0043 sgc=sgch+sgcv; % this is CORRECT ????
0044 
0045 ZavC=sum(Z.^2.*Zperc);% this is CORRECT ????
0046 
0047 sigmacoulombLocal=2*pi.*r0.^2.*ZavC.*sgc.*(me/E0).^2;% sum contribution for various atoms
0048 
0049 sigmacoulomb=mean(sigmacoulombLocal);
0050 
0051 sigmacoulomb=sigmacoulomb*10^4*10^24;% cross section from m^2 to barn, 1 barn=10^-24 cm^2
0052 
0053 
0054 % DEE is along the lattice. average of sigma along the lattice
0055 Zav=sum(Z.*(Z+1).*log(183./Z.^(1/3)).*Zperc);
0056 
0057 sigmabremsstrahlungLocal=16*alpha*r0^2/3.*Zav.*(log(1./DEE)-5/8);
0058 
0059 sigmabremsstrahlung=mean(sigmabremsstrahlungLocal);
0060 
0061 sigmabremsstrahlung=sigmabremsstrahlung*10^4*10^24;% cross section from m^2 to barn, 1 barn=10^-24 cm^2
0062 size(sigmabremsstrahlungLocal)
0063 size(sigmacoulombLocal)
0064 
0065 sigma=sigmabremsstrahlungLocal*10^4*10^24+sigmacoulombLocal*10^4*10^24; %in barn
0066 
0067 % n_mol=P./kboltz/T;%[m^-3] molar density of residual gas along the ring
0068 
0069 invtvac=P.*sigma./(0.474*T);
0070 
0071 tvac=length(sigma)/sum(invtvac);% h
0072 
0073