% gyroDispersionRelation.m
%   Plots dispersion relation for the gyrotron device and 
%   the resonance line for the TWT, CARM and BWO devices.
%
% Colin Joye, 6/25/03W
%
% run research/gyroDispersionRelation

c = 3e8;         % [m/s]  Speed of light
kz =[-1:0.01:1]; % [m^-1] Axial propagation constant range
kmn = sqrt(0.1); % [m^-1] Perpendicular propagation constant
s = 1;           % [integer] harmonic number

% Radian frequency computed from dispersion relation (red)
w = c * sqrt( kz.^2 + kmn^2 ); 
w1= c * abs( kz ); % speed of light line.

% BWO resonance line (green)
V0 = 10e3;            % [volts] Applied voltage
gamma=1+1.954e-6*V0   % [] relativistic gamma
vz=c*sqrt(1-1/gamma); % [m/s] axial electron velocity
omega=1.5*c*kmn;      % [rad/s] cycletron frequency
w_bwo=kz*vz+s*omega;  % TWT resonance line

% Gyro-TWT resonance line (cyan)
V0 = 15e3;            % [volts] Applied voltage
gamma=1+1.954e-6*V0   % [] relativistic gamma
vz=c*sqrt(1-1/gamma); % [m/s] axial electron velocity
omega=0.985*c*kmn;     % [rad/s] cycletron frequency
w_twt=kz*vz+s*omega;  % TWT resonance line

% CARM resonance line (blue)
V0 = 3.5e5;           % [volts] Applied voltage
gamma=1+1.954e-6*V0   % [] relativistic gamma
vz=c*sqrt(1-1/gamma); % [m/s] axial electron velocity
omega=0.8*c*kmn;      % [rad/s] cycletron frequency
w_carm=kz*vz+s*omega; % TWT resonance line

%[x_bwo,y_bwo]   = find_intersection(kz,w,w_bwo);
%[x_twt,y_twt]   = find_intersection(kz,w,w_twt);
%[x_carm,y_carm] = find_intersection(kz,w,w_carm);

figure(1)
clf(1)
hold on;
plot([kz(1) kz(end)],[0 0],'k',[0 0],[0 max(w)],'k');
plot(kz,w1,'k:',kz,w,'r',kz,w_bwo,'g',kz,w_twt,'c',kz,w_carm,'b');
%plot(x_bwo(1),y_bwo(1),'g.',x_twt,y_twt,'c.',x_carm,y_carm,'b.');
%grid on;
hold off;
axis([kz(1) kz(end) 0 max(w)]);
xlabel(['kz [m^-^1]']);
ylabel(['w [rad / s]']);
text(0.1,1.6e8,'BWO');
text(0.8,2.2e8,'CARM');
text(0.6,1.1e8,'TWT');
text(-0.6,2.2e8,'Disp. Rel.');


% -------END gyroDispersionRelation.m --------------------