DiocotronStability.m
479d4b67b232geom_testmumps

DiocotronStability.m
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			rbm=0.005;
			rbp=0.0128;
			%rbm=0.09;
			%rbp=0.113;
			%b=0.16;
			%a=0.001;
			a=M.rgrid(1);
			b=M.rgrid(end);

			Q=mean(M.Er(1,floor(length(M.zgrid)/2),end-30:end),3)/2*a;
			%Q=mean(M.Er(1,100,end-30:end),3)/2*a;
			omega_d=M.omepe^2/(2*M.omece);
			if( a~=0)
			omega_q=2Q/(M.B0(rbm^2));
			else
			omega_q=0;
			end

			Levaluated=10;
			stability=zeros(Levaluated,1);
			for l=1:Levaluated
			stability(l)=(-l(1-omega_q/omega_d)(1-(rbm/rbp)^2)(1-(a/b)^(2l))+ ...
			2(1+(a/b)^(2l))-(1+(rbm/rbp)^(2l))((a/rbm)^(2l)+(rbp/b)^(2l)))^2 -...
			4(rbm/rbp)^(2l)(1-(rbp/b)^(2l))^2(1-(a/rbm)^(2l))^2;
			if(stability(l) <0)
			fprintf(2,"Diocotron mode l=%d is potentially unstable\n",l);
			end
			end
			fig=figure;
			plot(1:Levaluated,stability)
			hold on
			plot([1 Levaluated],[0 0],'k')
			for l=1:Levaluated
			if stability(l)<0
			plot(l,stability(l),'rx')
			end
			end
			xlabel('azimuthal mode number')
			ylabel('stability condition')
			title(sprintf('r_b^-=%1.2g [m] r_b^+=%1.2g [m] a=%1.2g [m] b=%1.2g [m]',rbm,rbp,a,b))
			M.savegraph(fig,sprintf('%s/%s_diocstab',M.folder,M.name),[15,10])