-
Notifications
You must be signed in to change notification settings - Fork 52
/
12-limited.py
239 lines (181 loc) · 7.12 KB
/
12-limited.py
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
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
#!/usr/bin/env python
import freegs
import freegs.critical as critical
from freegs import geqdsk
from freegs.plotting import plotEquilibrium
import matplotlib.pyplot as plt
import numpy as np
'''
First creates a limited plasma and solves, before
creating a diverted plasma (which will have a larger CSA)
and solves under identical constraints. Due to the reduced CSA
of the limited plasma, one expects the plasma profiles to have a larger
magnitude when limited such that J is larger. J is expected to be larger
such that when J is integrated over a smaller CSA, the resultant Ip (and BetaP)
are the same. Consequently, different coil currents are also expected.
'''
#########################################
# Create the machine, which specifies coil locations
# and equilibrium, specifying the domain to solve over
tokamak = freegs.machine.TestTokamakLimited()
eq = freegs.Equilibrium(tokamak=tokamak,
Rmin=0.1, Rmax=2.0, # Radial domain
Zmin=-1.0, Zmax=1.0, # Height range
nx=65, ny=65, # Number of grid points
boundary=freegs.boundary.freeBoundaryHagenow) # Boundary condition
#########################################
# Plasma profiles
profiles = freegs.jtor.ConstrainBetapIp(eq,
0.15, # Plasma poloidal beta
2e5, # Plasma current [Amps]
2.0) # Vacuum f=R*Bt
#########################################
# Coil current constraints
#
# Specify locations of the X-points
# to use to constrain coil currents
xpoints = [(1.1, -0.6), # (R,Z) locations of X-points
(1.1, 0.8)]
isoflux = [(1.1,-0.6, 1.1,0.6),(1.1,-0.6,0.732,0.0426)] # (R1,Z1, R2,Z2) pair of locations
constrain = freegs.control.constrain(xpoints=xpoints, isoflux=isoflux)
#########################################
# Nonlinear solve
freegs.solve(eq,
profiles,
constrain,
show=True,
check_limited = True,
limit_it = 0)
# eq now contains the solution
print("Done!")
print("Plasma current: %e Amps" % (eq.plasmaCurrent()))
print("Plasma pressure on axis: %e Pascals" % (eq.pressure(0.0)))
print("Poloidal beta: %e" % (eq.poloidalBeta()))
# Currents in the coils
tokamak.printCurrents()
##############################################
# Final plot of equilibrium
axis = eq.plot(show=False)
eq.tokamak.plot(axis=axis, show=False)
constrain.plot(axis=axis, show=True)
###############################################
# Check that the core is masked correctly
fig, ax = plt.subplots()
ax.contour(eq.R,eq.Z,eq.psiN(),levels=30,colors='b')
ax.contour(eq.R,eq.Z,eq.psiN(),levels=[1.0],colors='orange')
ax.plot(eq.tokamak.wall.R,eq.tokamak.wall.Z,color='k')
opt, xpt = critical.find_critical(eq.R,eq.Z,eq.psi())
isoflux = np.array(
freegs.critical.find_separatrix(eq, ntheta=101, opoint=opt, xpoint=xpt, psi=eq.psi())
)
ind = np.argmin(isoflux[:, 1])
rbdry = np.roll(isoflux[:, 0][::-1], -ind)
rbdry = np.append(rbdry,rbdry[0])
zbdry = np.roll(isoflux[:, 1][::-1], -ind)
zbdry = np.append(zbdry, zbdry[0])
ax.plot(rbdry,zbdry,'rx')
ax.contourf(eq.R,eq.Z,eq.mask)
ax.set_aspect('equal')
ax.set_xlabel('R(m)')
ax.set_ylabel('Z(m)')
plt.show()
from freegs import geqdsk
with open("limited.geqdsk", "w") as f:
geqdsk.write(eq, f)
#########################################
# Create the machine, which specifies coil locations
# and equilibrium, specifying the domain to solve over
tokamak = freegs.machine.TestTokamak()
eq2 = freegs.Equilibrium(tokamak=tokamak,
Rmin=0.1, Rmax=2.0, # Radial domain
Zmin=-1.0, Zmax=1.0, # Height range
nx=65, ny=65, # Number of grid points
boundary=freegs.boundary.freeBoundaryHagenow) # Boundary condition
#########################################
# Plasma profiles
profiles = freegs.jtor.ConstrainBetapIp(eq2,
0.15, # Plasma poloidal beta
2e5, # Plasma current [Amps]
2.0) # Vacuum f=R*Bt
#########################################
# Coil current constraints
#
# Specify locations of the X-points
# to use to constrain coil currents
xpoints = [(1.1, -0.6), # (R,Z) locations of X-points
(1.1, 0.8)]
isoflux = [(1.1,-0.6, 1.1,0.6),(1.1,-0.6,0.732,0.0426)] # (R1,Z1, R2,Z2) pair of locations
#current_lims = [(-150000.0,140000.0),(0.0,65000.0),(-105000.0,0.0),(-60000.0,0.0)]
#total_current = 350000.0
constrain = freegs.control.constrain(xpoints=xpoints, isoflux=isoflux)#, current_lims=current_lims, max_total_current = total_current)
#########################################
# Nonlinear solve
freegs.solve(eq2,
profiles,
constrain,
show=True,
check_limited = True)
# eq now contains the solution
print("Done!")
print("Plasma current: %e Amps" % (eq2.plasmaCurrent()))
print("Plasma pressure on axis: %e Pascals" % (eq2.pressure(0.0)))
print("Poloidal beta: %e" % (eq2.poloidalBeta()))
# Currents in the coils
tokamak.printCurrents()
##############################################
# Final plot of equilibrium
axis = eq2.plot(show=False)
eq2.tokamak.plot(axis=axis, show=False)
constrain.plot(axis=axis, show=True)
plt.show()
###############################################
# Check that the core is masked correctly
fig, ax = plt.subplots()
ax.contour(eq2.R,eq2.Z,eq2.psiN(),levels=30,colors='b')
ax.contour(eq2.R,eq2.Z,eq2.psiN(),levels=[1.0],colors='orange')
ax.plot(eq2.tokamak.wall.R,eq2.tokamak.wall.Z,color='k')
opt, xpt = critical.find_critical(eq2.R,eq2.Z,eq2.psi())
mask = critical.core_mask(eq2.R,eq2.Z,eq2.psi(),opt,xpt,eq2.psi_bndry)
ax.contourf(eq2.R,eq2.Z,mask)
ax.set_aspect('equal')
ax.set_xlabel('R(m)')
ax.set_ylabel('Z(m)')
plt.show()
#################
# Compare plasma profiles between limited and diverted plasmas
psi_levels = np.linspace(0.0,1.0,100,endpoint=True)
fig, ax = plt.subplots()
ax.plot(psi_levels,eq.pprime(psi_levels),color='r',label='limited')
ax.plot(psi_levels,eq2.pprime(psi_levels),color='b',label='diverted')
ax.set_xlabel('psiN')
ax.set_ylabel('pprime')
ax.legend()
plt.show()
fig, ax = plt.subplots()
ax.plot(psi_levels,eq.pressure(psi_levels),color='r',label='limited')
ax.plot(psi_levels,eq2.pressure(psi_levels),color='b',label='diverted')
ax.set_xlabel('psiN')
ax.set_ylabel('p')
ax.legend()
plt.show()
fig, ax = plt.subplots()
ax.plot(psi_levels,eq.ffprime(psi_levels),color='r',label='limited')
ax.plot(psi_levels,eq2.ffprime(psi_levels),color='b',label='diverted')
ax.set_xlabel('psiN')
ax.set_ylabel('ffprime')
ax.legend()
plt.show()
fig, ax = plt.subplots()
ax.plot(psi_levels,eq.fpol(psi_levels),color='r',label='limited')
ax.plot(psi_levels,eq2.fpol(psi_levels),color='b',label='diverted')
ax.set_xlabel('psiN')
ax.set_ylabel('fpol')
ax.legend()
plt.show()
#########################
# Load in the geqdsk of the limited plasma
tokamak = freegs.machine.TestTokamakLimited()
with open("limited.geqdsk") as f:
eq3 = geqdsk.read(f, tokamak, show=True)
# Plot equilibrium
plotEquilibrium(eq3)