Evaluates Eq. 18 in Rosenbluth Putvinski NF 1997 as a function of alpha or Zi INPUT: - epsi: inverse aspect ratio r/R - ne: plasma density for collision time calculation - alpha: E/Ec, vector - Zi: charge, vector OUTPUT: - Analytic runaway rate from Eq. 18 in Rosenbluth Putvinski NF 1997 by E. Nilsson (emelie.nilsson@cea.fr) Y. Peysson (CEA-DRFC) (yves.peysson@cea.fr) and J. Decker (CEA-DRFC) (joan.decker@cea.fr)
0001 function [RR_an] = RR_rosenbluth_en(alpha, Zi, ne, lnc_e_ref, epsi) 0002 % 0003 % Evaluates Eq. 18 in Rosenbluth Putvinski NF 1997 as a function of alpha 0004 % or Zi 0005 % 0006 % INPUT: 0007 % - epsi: inverse aspect ratio r/R 0008 % - ne: plasma density for collision time calculation 0009 % - alpha: E/Ec, vector 0010 % - Zi: charge, vector 0011 % 0012 % OUTPUT: 0013 % 0014 % - Analytic runaway rate from Eq. 18 in Rosenbluth Putvinski NF 1997 0015 % 0016 % by E. Nilsson (emelie.nilsson@cea.fr) Y. Peysson (CEA-DRFC) (yves.peysson@cea.fr) and J. Decker (CEA-DRFC) (joan.decker@cea.fr) 0017 % 0018 [qe,me,dummy,dummy,e0,dummy,dummy,dummy,clum] = pc_dke_yp; %Universal physics constants 0019 % 0020 %tau_c = me^2*clum^3/(4*pi*ne*qe^4*lnl) 0021 tau_c = 4*pi*e0^2*me^2*clum^3/(ne*qe^4*lnc_e_ref); %LUKE def. 0022 %Ec=me*clum/(qe*tau_c); 0023 % 0024 gam = 1/(1+1.47*sqrt(epsi)+1.72*epsi); 0025 %alpha = alpha/1e4*clum; 0026 if Zi == -1 0027 RR_an = 1/(2*tau_c*lnc_e_ref).*(alpha-1); %simplified growth rate, for E/Ec >> 1, see 0028 elseif Zi>1 0029 b= 2*gam/(3*(Zi+1)).*alpha.^2; 0030 RR_an = 1/(tau_c*lnc_e_ref).*sqrt(pi.*b/2).*sqrt(1+8*pi./(9*b)); %simplified growth rate, for E/Ec >> 1, see 0031 else 0032 RR_an = 1/(tau_c*lnc_e_ref)*sqrt((pi*gam)./(3*(Zi+5))).*(alpha-1)./sqrt((1-1./alpha+4*pi*(Zi+1).^2./(3*gam*(Zi+5).*(alpha.^2+4/gam^2-1)))); 0033 end 0034 %small E/Ec 0035 %RR_an = 1/(tau_c*(Zi+1)*lnc_e_ref).*alpha.*(alpha-1); %simplified growth rate, for E/Ec >> 1, see 0036 0037 0038 %Eq (7) in RP NF 1997 0039 %