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nonlindioc/matlab/analytic_growth.m
0b252c046024master

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analytic_growth.m
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function gamma = analytic_growth(l,a,b,phia,phib,B0,n0,rm,rp)
% Physical constants
e=1.602176634e-19;
eps0=8.854188e-12;
q=-e;
wD=n0*e/(2*eps0*B0); % diocotron frequency
phim=1/log(b/a)*(-q*n0*rm^2/2/eps0*log(rm/a)*log(rp/rm)+(phib+q*n0/2/eps0*(rp^2-rm^2)*(log(b/rp)+0.5))*log(rm/a)+phia*log(b/rm));
Q=(phia-phim)/(2*log(rm/a)); % charge per unit length on the inner electrode
wq=-2*Q/(B0*rm^2); % angular velocity at r = rm
bl=(l*((1-(rm/rp)^2)+ (wq/wD)*(1+(rm/rp)^2))*(1-(a/b)^(2*l)) + ...
(1-(rm/rp)^(2*l))*((rp/b)^(2*l) - (a/rm)^(2*l)))/(1-(a/b)^(2*l));
cl=(l^2*(wq/wD)*(1-(rm/rp)^2 + (wq/wD)*(rm/rp)^2)*(1-(a/b)^(2*l)) - ...
l*(wq/wD)*(1-(a/rp)^(2*l))*(1-(rp/b)^(2*l)) + l*(1-(rm/rp)^2 + ...
(wq/wD)*(rm/rp)^2)*(1-(a/rm)^(2*l))*(1-(rm/b)^(2*l)) - ...
(1-(a/rm)^(2*l))*(1-(rp/b)^(2*l))*(1-(rm/rp)^(2*l)))/(1-(a/b)^(2*l));
w1=wD/2*(bl-sqrt(bl^2-4*cl));
w2=wD/2*(bl+sqrt(bl^2-4*cl));
gamma=imag(w2);
end
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