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sct_eigsolve.py
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# -*- coding: utf-8 -*-
import numpy as np
def eigsolve(MM,zed,nzh,electromagnetic,pin):
soln = np.linalg.eig(MM)
E0 = soln[0] # the eigenvalues (E0 = -i omega = d/dt)
indices = np.argsort(E0.real) # sort by growth rate
E = soln[0][indices] #get the eigenvalues into order
eigfns = soln[1][:,indices] #get the eigenvectors into order
# determine number of unstable modes to write output
# or write out the 5 slowest decaying modes
nmodes = E.size
nunstable = 0
for imode in range(0,nmodes):
if (E[imode].real > 0):
omega = 1j*E[imode]
#print("mode ",imode, "-i omega = ",E[imode],"\n")
#print("mode ",imode, " omega = ",omega,"\n")
nunstable = nunstable + 1
if(nunstable == 0):
ndiag = 5
else:
ndiag = nunstable
omega = np.zeros(ndiag,dtype=complex)
for imode in range(0,ndiag):
omega[imode] = 1j*E[imode+nmodes-ndiag]
print("mode ",imode, " omega = ",omega[imode],"\n")
if(electromagnetic):
dens, temp, current, zed_out = get_electromagnetic_eigfns(eigfns[:,nmodes-ndiag:],zed,nzh,pin,omega)
else:
dens, temp, current, zed_out = get_electrostatic_eigfns(eigfns[:,nmodes-ndiag:],zed,nzh,pin)
return omega, dens, temp, current, zed_out
def get_electromagnetic_eigfns(eigfns,zed,nzh,pin,omega,test=False):
nzed = zed.size
[wstarn,wstart,tite,shat,beta,a0,a1,a2,d0,d1,d2,f0,wdrift,b0,b1,b2,b3,m0,m1,m2,m3] = pin
[nmatrix,nmodes] = np.shape(eigfns)
ized_current = nmatrix - 1
ized_dzp = nzh
ized_dzm = nzh - 1
Dzed = zed[ized_dzp]
#print(Dzed)
zed_full = np.zeros([nzed+2])
zed_full[:nzh] = zed[:nzh]
zed_full[nzh+2:] = zed[nzh:]
#print("zed_full",zed_full)
dens_full = np.zeros( [nzed+2,nmodes],dtype=complex)
temp_full = np.zeros( [nzed+2,nmodes],dtype=complex)
current = np.zeros(nmodes,dtype=complex)
for imode in range(0,nmodes):
dens = eigfns[0:nzed,imode]
imax = np.argmax(np.abs(dens))
norm = dens[imax]
dens = dens/norm
temp = eigfns[nzed:2*nzed,imode]/norm
current[imode] = eigfns[ized_current,imode]/norm
# postprocessing using imposed bc.
dens0p = ( -(2./3.)*(Dzed/a0)*current[imode] + (4./3.)*dens[ized_dzp] - (1./3.)*dens[ized_dzp+1]
+ (a1/a0)*( (2./3.)*(temp[ized_dzp]-temp[ized_dzm]) + (1./6.)*(temp[ized_dzm-1]-temp[ized_dzp+1]) ) - (a1/a0)*( 1j*np.pi*beta*wstart*current[imode]/(2.*shat) ) )
dens0m = -dens0p + (4./3.)*(dens[ized_dzp] + dens[ized_dzm]) - (1./3.)*(dens[ized_dzp+1] + dens[ized_dzm-1])
temp0m = (2./3.)*(temp[ized_dzm] + temp[ized_dzp]) - (1./6.)*(temp[ized_dzm-1] + temp[ized_dzp+1]) - 1j*np.pi*beta*wstart*current[imode]/(2.*shat)
temp0p = (2./3.)*(temp[ized_dzm] + temp[ized_dzp]) - (1./6.)*(temp[ized_dzm-1] + temp[ized_dzp+1]) + 1j*np.pi*beta*wstart*current[imode]/(2.*shat)
if(test):
#temp0prim = (4.*temp[ized_dzp] - 3.*temp0p - temp[ized_dzp+1])/(2.*Dzed)
temp0prim = (4.*(temp[ized_dzp]-temp[ized_dzm]) - 3.*(temp0p-temp0m) - temp[ized_dzp+1] + temp[ized_dzm-1])/(4.*Dzed)
#dens0prim = (4.*dens[ized_dzp] - 3.*dens0p - dens[ized_dzp+1])/(2.*Dzed)
dens0prim = (4.*(dens[ized_dzp]-dens[ized_dzm]) - 3.*(dens0p-dens0m) - dens[ized_dzp+1] + dens[ized_dzm-1])/(4.*Dzed)
current_post = a0*dens0prim + a1*temp0prim
print("sanity check comparisons of neighbouring grid points -- not second order accurate! \n ")
print("dens0prim",dens0prim,"(dens[ized_dzp+1]-dens[ized_dzp])/Dzed,",(dens[ized_dzp+1]-dens[ized_dzp])/Dzed,
"(dens[ized_dzm]-dens[ized_dzm-1])/Dzed,",(dens[ized_dzm]-dens[ized_dzm-1])/Dzed)
print("temp0prim",temp0prim,"(temp[ized_dzp+1]-temp[ized_dzp])/Dzed,",(temp[ized_dzp+1]-temp[ized_dzp])/Dzed,
"(temp[ized_dzm]-temp[ized_dzm-1])/Dzed,",(temp[ized_dzm]-temp[ized_dzm-1])/Dzed)
print("n(Dz)-n(-Dz)",dens[ized_dzp]-dens[ized_dzm],"n(0+)-n(0-)",dens0p-dens0m)
print("T(Dz)-T(-Dz)",temp[ized_dzp]-temp[ized_dzm],"T(0+)-T(0-)",temp0p-temp0m)
print("\n")
print("Check b.c. using second order accurate formulas \n")
print("J",current[imode],"a0*dens0prim + a1*temp0prim",current_post)
print("n(0+)-n(0-)",dens0p-dens0m, "1j*np.pi*beta*(wstarn-omega)*current/shat",1j*np.pi*beta*(wstarn-omega[imode])*current[imode]/shat)
print("T(0+)-T(0-)",temp0p-temp0m, "1j*np.pi*beta*wstart*current/shat",1j*np.pi*beta*wstart*current[imode]/shat)
print("\n")
dens_full[:nzh,imode] = dens[:nzh]
dens_full[nzh,imode] = dens0m
dens_full[nzh+1,imode] = dens0p
dens_full[nzh+2:,imode] = dens[nzh:]
temp_full[:nzh,imode] = temp[:nzh]
temp_full[nzh,imode] = temp0m
temp_full[nzh+1,imode] = temp0p
temp_full[nzh+2:,imode] = temp[nzh:]
return dens_full, temp_full, current, zed_full
def get_electrostatic_eigfns(eigfns,zed,nzh,pin):
nzed = zed.size
[wstarn,wstart,tite,shat,beta,a0,a1,a2,d0,d1,d2,f0,wdrift,b0,b1,b2,b3,m0,m1,m2,m3] = pin
[nmatrix,nmodes] = np.shape(eigfns)
ized_dzp = nzh + 1
ized_dzm = nzh - 1
#print(zed[ized_dzm])
#print(zed[ized_dzp])
#print(zed)
Dzed = zed[ized_dzp]
dens_full = np.zeros( [nzed,nmodes],dtype=complex)
temp_full = np.zeros( [nzed,nmodes],dtype=complex)
current = np.zeros(nmodes,dtype=complex)
for imode in range(0,nmodes):
dens = eigfns[0:nzed,imode]
imax = np.argmax(np.abs(dens))
norm = dens[imax]
dens_full[:,imode] = dens/norm
temp_full[:,imode] = eigfns[nzed:2*nzed,imode]/norm
current[imode] = (a0*(dens_full[ized_dzp,imode]-dens_full[ized_dzm,imode])+ a1*(temp_full[ized_dzp,imode]-temp_full[ized_dzm,imode]) )/(2.*Dzed)
return dens_full, temp_full, current, zed