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fennecslite/magnet/Cryogenic/r_beam_Cryogenic_170.m
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r_beam_Cryogenic_170.m
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function r_beam = r_beam_Cryogenic_170(magnet,I)
%
% function r_beam = r_beam_Cryogenic_170(magnet,I)
%
% Ex: >> r_beam = r_beam_Cryogenic_170('cryogenic',[57.712 , 68.596 , 107.780 , 107.780])
%
% Returns an estimate of the electron beam radius in the cavity of the GT140 gyrotron
%%
% Version: 1.0 J.-P. Hogge Feb. 27, 2008
% 1.1 J.-P. Hogge Nov. 23, 2011 : Refurbished first prototype parameters
% 2.0 J.-P. Hogge Aug. 10th, 2017 : Estimation based on elliptical integrals only (a bit more complicated, but more precise)
% 2.1 J.-P. Hogge Jun. 7th, 2018 : corrected minor bug (so far only cryogenic magnet was implemented.
%
%
% magnet : 'cryogenic' or any other 170GHz magnet
%
%
% Procedure:
% ----------
%
% First the azimuthal component aphi of the vector potential is computed at the cathode.
% Then the axial component of the magnetic field in the vicinity of the axis, and
% in the cavity region is estimated.
% By applying flux conservation, the beam radius is estimated.
%
%****************************************************************************************
% rcat = 0.05318; % Cathode center radius [m] 1st 1MW Prototype, cold dimension (2017)
% rcat = 0.0533693; % Cathode center radius [m] 1st 1MW Prototype, warm dimension (2017)
% zcat = 0.136; % Cathode center location [m] Refurbished Prototype (2011)
% zcav = 0.4995; % Cavity location [m]
%
GT170_1MW_Geometry
% Compute vector potential aphi at cathode location
[Aphi] = B_Ellip_Cryogenic_170('aphi',magnet,I,r_cat,z_cat);
% flux = 2 * pi * rcat * Aphi;
% Compute axial magnetic field and its derivatives in cavity
% [Bzcav,dBzcav,d2Bzcav] = B_on_axis_170('asg_modified_201206',I,zcav);
Bzcav = B_Ellip_Cryogenic_170('bz', magnet,I,0,z_cav);
dBzcav = B_Ellip_Cryogenic_170('dbzdz', magnet,I,0,z_cav);
d2Bzcav = B_Ellip_Cryogenic_170('d2bzdz2',magnet,I,0,z_cav);
%
% Apply flux conservation to find beam radius in cavity
% The exact flux at cathode (r_cat * Aphi) is equalled to the flux
% estimated with paraxial expansion.
%
a = 1/16 * d2Bzcav;
b = - Bzcav/2;
c = r_cat * Aphi;
rbsq_plus = 1./(2*a) * (-b + sqrt(b^2 - 4*a*c));
rbsq_minus = 1./(2*a) * (-b - sqrt(b^2 - 4*a*c));
r_beam = sqrt(rbsq_minus);
%
% Estimation based on elliptical integrals only.
% The following equation is solved for r_beam:
% r_cat * Aphi(r_cat,z_cat) = r_beam * Aphi(r_beam,z_cav)
%
raphi_cat = r_cat * Aphi;
myfun = @(r,z_cav,I,raphi_cat) r*B_Ellip_Cryogenic_170('aphi',magnet,I,r,z_cav)-raphi_cat;
fun = @(r) myfun(r,z_cav,I,raphi_cat);
r_beam = fzero(fun, 0.009);
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