-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathcbspec_old.m
220 lines (192 loc) · 9.16 KB
/
cbspec_old.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
%% Numerically integrates P_i(f,\theta)=\int dk^3 P_i(k) \delta(2\pi f - k*v)
%% for given kx(=2pi f/v, kx is in rotated frame with kx||v) and \theta
%% Model of P_i(k) is critically balanced with k_para~L^(1/3)k_perp^(2/3) in ion
%% inertial range and k_\para~L^(1/3)\rho^(1/3)k_\perp^(1/3) in electron inertial range
%% P_i(k) as described in Cho et al., 2002 (ApJ)
%%
%% Author: Michael von Papen
%% Date: 26.06.2013
function [P,kern] = cbspec (f,theta,n,fun,L0,rho,v,va,B,bounds,ratioTP,rhoe,si_in,cb_in,mirror)
%% Check Input
if nargin<15; mirror=0; end
if nargin<14; cb_in=[2/3 1/3]; end
if nargin<13; si_in=[-10/3 -11/3]; end
if nargin<11; ratioTP=0; end
if nargin<10; bounds=[-10 1]; end
if nargin<9; B=1e-9; end
if nargin<8; va=60e3; end
if nargin<7; v=600e3; end
if nargin<6; rho=1e5; end
if nargin<5; L0=1e9; end
if nargin<4; fun=1; end
if nargin<3; n=500; end
if nargin<2; theta=[0 90]; end
if nargin<12; rhoe=rho/42.85; end
%% Wave vector in rotated coordinate system
kix=2*pi*f/v;
%% Basic Parameter
si=si_in(1); %-10/3->k^{-5/3}
si2=si_in(2); %-11/3->k^{-7/3}
cb=cb_in(1); % 2/3->alfven
cb2=cb_in(2); %1/3->KAW
%% K-space gridpoints
% Set boundaries a little bit wider than kmin,kmax for numerical reasons.
% Later everything outside [kmin,kmax] will be disregarded
kmin=bounds(1);
kmax=bounds(2);
ky=10.^[kmin+(0:n-2)*(kmax-kmin)/(floor(n)-1), kmax];
dky=[ky(2:end) 2*10^kmax]-ky;
%nz log verteilt auf pos UND neg Achse
kiz=repmat([-ky(end:-1:1) ky],n,1);
dkiz=repmat([dky(end:-1:1) dky],n,1);
ky=ky(ones(1,2*n),:)'; % <=> ky=repmat(ky',1,2*n);
dky=dky(ones(1,2*n),:)';
% %% Ion-cyclotron frequency cut-off
% % All k_para ~ w_ic/V_A are subject to ion-cyclotron damping
% % Thus, parallel scales cannot reach k_para > w_ic/V_A
% if nargin<6;
kz_max=kmax;
% else
% kz_max=min([kmax log10(1.6e-19*B/1.67e-27/va)]);
% end
%% Set output variable
if ratioTP ~=0
P=zeros(4,length(kix),length(theta));
else
P=zeros(length(kix),length(theta));
end
%% Begin with loop over theta
for k=1:length(theta)
%% Begin loop over frequency
for i=1:length(kix)
%% Calculate PSD at z
kx=kix(i)*sind(theta(k))-kiz.*cosd(theta(k)); %=kx in unrotated system
%ky=kiy in unrotated system
kz=kix(i)*cosd(theta(k))+kiz.*sind(theta(k)); %=kz in unrotated system
kern=zeros(n,2*n);
kp2=ky.^2+kx.^2; % k_perp^2
kabs2=kp2+kz.^2; % |k|
% cbetaT=cbetaT
%% Equations written in unprimed coordinates for the sake of
%% brevity, but integration is done over primed variables,
%% which is why dkiy and dkiz is used.
for L=L0
%% Single components Alfven cascade
i1=find(kp2 <= 1/rho^2 & kp2 > 1/L^2 & abs(kz) <= 10^kz_max ...
& kabs2 <= 10^(2*kmax));
switch fun
case 1 %'exp'
kern( i1 ) = kern(i1) + kp2(i1).^(si/2)...
.*exp(-L^(1-cb).*abs(kz(i1))./kp2(i1).^(cb/2))...
.*dky(i1).*dkiz(i1);
case 2 %'expdamp' for Ti=Te => rho_e=sqrt(me/mi)*rho_i
kern( i1 ) = kern(i1) + kp2(i1).^(si/2)...
.*exp(-L^(1-cb).*abs(kz(i1)./kp2(i1).^(cb/2))...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1);
case 3 %'gauss'
kern( i1 ) = kern(i1) + kp2(i1).^(si/2)...
.*exp(-(L^(1-cb)*abs(kz(i1))./kp2(i1).^(cb/2)-1).^2)...
.*dky(i1).*dkiz(i1)/sqrt(pi);
case 4 %'gaussdamp'
kern( i1 ) = kern(i1) + kp2(i1).^(si/2)...
.*exp(-(L^(1-cb)*abs(kz(i1))./kp2(i1).^(cb/2)-1).^2 ...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1)/sqrt(pi);
case 5 %'heavi'
i2=find(L^(1-cb)*abs(kz(i1)./kp2(i1).^(cb/2))<=1);
kern( i1(i2) ) = kern(i1(i2)) + kp2(i1(i2)).^(si/2).*dky(i1(i2)).*dkiz(i1(i2));
case 6 %'delta'
[tmp,i2]=min((L^(1-cb)*abs(kz(i1))-kp2(i1).^(cb/2)).^2);
kern( i1(i2) ) = kern(i1(i2)) + L^(1-cb).*kp2(i1(i2)).^(si/2)...
.*dky(i1(i2)).*dkiz(i1(i2));
case 7 %'expisodamp'
kern( i1 ) = kern(i1) + kp2(i1).^(si/2)...
.*exp(-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1);
end
%% Single components KAW cascade
i1=find(kp2 > 1/rho^2 & kp2 > 1/L^2 & abs(kz) <= 10^kz_max ...
& kabs2 <= 10^(2*kmax) & kp2 <= 1/rhoe^2);
switch fun
case 1 %'exp'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))./kp2(i1).^(cb2/2) )...
.*dky(i1).*dkiz(i1);
case 2 %'expdamp' for Ti=Te => rho_e=sqrt(me/mi)*rho_i
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))./kp2(i1).^(cb2/2)...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1);
case 3 %'gauss'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))./kp2(i1).^(cb2/2)-1).^2)...
.*dky(i1).*dkiz(i1)/sqrt(pi);
case 4 %'gaussdamp'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))./kp2(i1).^(cb2/2)-1).^2 ...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1)/sqrt(pi);
case 5 %'heavi'
i2=find(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))./kp2(i1).^(cb2/2)<=1);
kern( i1(i2) ) = kern(i1(i2)) + rho^(si2-si).*kp2(i1(i2)).^(si2/2)...
.*dky(i1(i2)).*dkiz(i1(i2));
case 6 %'delta'
[tmp,i2]=min((L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))-kp2(i1).^(cb2/2)).^2);
kern( i1(i2) ) = kern(i1(i2)) + L^(1-cb)*rho^(si2-si).*kp2(i1(i2)).^(si2/2)...
.*dky(i1(i2)).*dkiz(i1(i2));
case 7 %'expisodamp'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp(-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1);
end
%% Single components of cascade at electron scales
i1=find(kp2 > 1/rhoe^2 & abs(kz) <= 10^kz_max ...
& kabs2 <= 10^(2*kmax));
switch fun
case 1 %'exp'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))*rhoe^cb2 )...
.*dky(i1).*dkiz(i1);
case 2 %'expdamp' for Ti=Te => rho_e=sqrt(me/mi)*rho_i
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))*rhoe^cb2...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1);
case 3 %'gauss'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))*rhoe^cb2-1).^2)...
.*dky(i1).*dkiz(i1)/sqrt(pi);
case 4 %'gaussdamp'
kern( i1 ) = kern(i1) + rho^(si2-si).*kp2(i1).^(si2/2)...
.*exp( -(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))*rhoe^cb2-1).^2 ...
-sqrt(kp2(i1))*rhoe).*dky(i1).*dkiz(i1)/sqrt(pi);
case 5 %'heavi'
i2=find(L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))*rhoe^cb2<=1);
kern( i1(i2) ) = kern(i1(i2)) + rho^(si2-si).*kp2(i1(i2)).^(si2/2)...
.*dky(i1(i2)).*dkiz(i1(i2));
case 6 %'delta'
[tmp,i2]=min((L^(1-cb)*rho^(cb-cb2)*abs(kz(i1))-rhoe^cb2).^2);
kern( i1(i2) ) = kern(i1(i2)) + L^(1-cb)*rho^(si2-si).*kp2(i1(i2)).^(si/2)...
.*dky(i1(i2)).*dkiz(i1(i2));
end
end
%% Full version with Toroidal and Poloidal parts
% Sum up to get power for one ky value
if ratioTP ~= 0
Tor=ratioTP/(1+ratioTP)*kern./kp2;
Pkern=kern;
% Add mirror modes to Pkern %WIP
if mirror~=0
sigma=0.2; sigmaz=1e-7/rho;
i1=find(kz.^2./kp2<1e-2);
Pkern(i1)=Pkern(i1)+mirror/(2*pi*sqrt(sigma*sigmaz))...
*exp(-log10(10*sqrt(kp2(i1))*rho).^2/2/sigma^2 ...
-kz(i1).^2/2/sigmaz).*dky(i1).*dkiz(i1);
end
Pol=(1-ratioTP/(1+ratioTP))*Pkern./kabs2;
P(1,i,k)=sum(sum( ky.^2.*Tor ...
+(kx.*kz).^2./kp2.*Pol ));
P(2,i,k)=sum(sum( kx.^2.*Tor ...
+(ky.*kz).^2./kp2.*Pol ));
P(3,i,k)=sum(sum( kp2.*Pol ));
P(4,i,k)=sum(P(1:3,i,k));
else
P(i,k)=sum(sum(2*kern));
end
end
end
P=1/v/L^(1-cb).*P;