def getDispersionGyro1(theta, eta, kx, ky, doGyro1=False):
from PyPPL import PlasmaDispersion, getZero, Gamma0,Gamma1
from numpy import exp
kp = np.sqrt(2.) * theta * ky
b = kx**2 + ky**2
kyp = ky/kp
lambda_D2 = 0.
G0 = Gamma0(b)
G0mG1 = Gamma0(b) - Gamma1(b)
def DR_Gyro(w):
zeta = w / kp
Z = PlasmaDispersion(zeta)
if (doGyro1):
Lambda = lambda_D2 * b + exp(b) * (1. + 1. - G0)
R = - (1. - eta/2. * (1. + b))*kyp * Z \
- eta * kyp * (zeta + zeta**2 * Z) + zeta * Z + 1. + Lambda
else :
Lambda = lambda_D2 *b + (1. - G0) + 1.
R = - (1. - eta/2.)*kyp * G0 * Z + eta * kyp * b * G0mG1 * Z \
- eta * kyp * G0 * ( zeta + zeta**2 * Z) + zeta * Z * G0 + G0 + Lambda
return R
# Take care of extra pie due to normalization
if ky > 0.33 : init = [0.05+0.05j, 0.0+0.0j, 0.1+0.1j]
elif ky < 0.15 : init = [0.01+0.01j, -0.01+0.01j, 0.0+0.0j]
else : init = [0.000+0.04j, 0.002+0.045j, 0.001+0.035j]
return getZero(DR_Gyro, init=init)
def getDispersionGyro1(theta, eta, kx, ky, doGyro1=False):
from PyPPL import PlasmaDispersion, getZero, Gamma0, Gamma1
from numpy import exp
kp = np.sqrt(2.) * theta * ky
b = kx**2 + ky**2
kyp = ky / kp
lambda_D2 = 0.
G0 = Gamma0(b)
G0mG1 = Gamma0(b) - Gamma1(b)
def DR_Gyro(w):
zeta = w / kp
Z = PlasmaDispersion(zeta)
if (doGyro1):
Lambda = lambda_D2 * b + exp(b) * (1. + 1. - G0)
R = - (1. - eta/2. * (1. + b))*kyp * Z \
- eta * kyp * (zeta + zeta**2 * Z) + zeta * Z + 1. + Lambda
else:
Lambda = lambda_D2 * b + (1. - G0) + 1.
R = - (1. - eta/2.)*kyp * G0 * Z + eta * kyp * b * G0mG1 * Z \
- eta * kyp * G0 * ( zeta + zeta**2 * Z) + zeta * Z * G0 + G0 + Lambda
return R
# Take care of extra pie due to normalization
if ky > 0.33: init = [0.05 + 0.05j, 0.0 + 0.0j, 0.1 + 0.1j]
elif ky < 0.15: init = [0.01 + 0.01j, -0.01 + 0.01j, 0.0 + 0.0j]
else: init = [0.000 + 0.04j, 0.002 + 0.045j, 0.001 + 0.035j]
return getZero(DR_Gyro, init=init)
def getDispersion(ky, parameters):
from PyPPL import PlasmaDispersion, getZero, Gamma0, Gamma1
from numpy import exp
mode = parameters['mode']
m_ie = parameters['m_ie']
tau = parameters['tau']
kx = parameters['kx']
kp = parameters['kp']
beta = parameters['beta']
lambda_D = parameters['lambdaD']
rhoLn = parameters['rhoLn']
rhoLT = parameters['rhoLT']
def DR_Smoly(w):
k_ortho2 = kx**2 + ky**2
mass_e = 1. / m_ie
# ion diamagnetic frequency
w_ni = -ky / kp * rhoLn * 0.5
w_Ti = -ky / kp * rhoLT * 0.5
s_i = w
b_i = (kx**2 + ky**2) / 2.
w_ni = -ky / kp * rhoLn
w_Ti = -ky / kp * rhoLT
s_i = w / sqrt(2.)
b_i = (kx**2 + ky**2)
#electron
w_ne = ky / kp * rhoLn
w_Te = ky / kp * rhoLT
s_e = w / sqrt(2. / mass_e)
b_e = (kx**2 + ky**2) * mass_e
# Plasma skin depth
delta = tau / (beta) / m_ie #sqrt(m_ie)
######################## Dispersion relation for gyrokinetic EM mode
# settings for the ions
Gamma_0i = Gamma0(b_i)
Gamma_1i = Gamma1(b_i)
Z_i = PlasmaDispersion(s_i)
l_i = 1. - (1. - w_ni / w) * Gamma_0i - w_Ti / w * (Gamma_0i -
Gamma_1i) * b_i
D_i = (1. - w_ni/w) * ( 1. + s_i * Z_i) * Gamma_0i + w_Ti/w * s_i * \
(0.5 * Z_i - s_i - s_i**2 * Z_i ) * Gamma_0i \
+ w_Ti/w * ( 1. + s_i * Z_i) * ( Gamma_0i - Gamma_1i) * b_i
# settings for the electrons
Gamma_0e = Gamma0(b_e)
Gamma_1e = Gamma1(b_e)
Z_e = PlasmaDispersion(s_e)
l_e = 1. - (1. - w_ne / w) * Gamma_0e - w_Te / w * (Gamma_0e -
Gamma_1e) * b_e
D_e = (1. - w_ne/w) * ( 1. + s_e * Z_e) * Gamma_0e + w_Te/w * s_e * \
(0.5 * Z_e - s_e - s_e**2 * Z_e ) * Gamma_0e \
+ w_Te/w * ( 1. + s_e * Z_e) * ( Gamma_0e - Gamma_1e) * b_e
#############################################################
# Standard Dispersion relation
if (mode == "EM"):
d = k_ortho2 * delta**2 * (l_i * tau + l_e + D_i * tau + D_e ) - 2 * s_e**2 * (D_i * tau + D_e) * (l_i * tau + l_e ) \
+ k_ortho2 * lambda_D**2 * ( k_ortho2 * delta**2 - 2 * s_e**2 * (D_i * tau + D_e))
# approximation for electrons
elif (mode == "ETG"):
d = 1. + l_e + D_e + lambda_D**2 * k_ortho2
# bad charge is wrong sign
elif (mode == "ITG"):
d = 1. + l_i + D_i + lambda_D**2 * k_ortho2
# simplified ITG dispersion relation
# approximation for electrons
elif (mode == "ITGe"):
d = l_e + D_e + tau * (l_i + D_i)
else:
raise NameError('No such Dispersion Relation')
return d
# Take care of extra pie due to normalization
if (mode == "EM"):
#init, solver = (-0.01 +.005j, -0.015 + 0.008j, 0.008 + 0.002j), 'muller'
init, solver = (-0.1 + .05j, -0.2 + 0.08j, -0.00 + 0.02j), 'muller'
if ky < 2.:
init, solver = (0.02 - .02j, 0.04 + 0.04j, 0.01 - 0.0j), 'muller'
else:
#goes init, solver = ( -0.4 - .012j, -0.1 - 0.03j, -0.2 - 0.012j), 'muller'
init, solver = (-0.4 - .012j, -0.1 - 0.03j,
-0.2 - 0.012j), 'muller'
else:
init, solver = (0.01 + .0026j, 0.02 + 0.03j, 0.015 + 0.01j), 'muller'
#init, solver = 0.01 + .03j, 'muller'
return getZero(DR_Smoly, init=init, solver=solver)
def getDispersion(ky, parameters):
from PyPPL import PlasmaDispersion, getZero, Gamma0,Gamma1
from numpy import exp
mode = parameters['mode']
m_ie = parameters['m_ie']
tau = parameters['tau']
kx = parameters['kx']
kp = parameters['kp']
beta = parameters['beta']
lambda_D = parameters['lambdaD']
rhoLn = parameters['rhoLn']
rhoLT = parameters['rhoLT']
def DR_Smoly(w):
k_ortho2 = kx**2 + ky**2
mass_e = 1./m_ie
# ion diamagnetic frequency
w_ni = - ky/kp * rhoLn * 0.5
w_Ti = - ky/kp * rhoLT * 0.5
s_i = w
b_i = (kx**2 + ky**2)/ 2.
w_ni = - ky/kp * rhoLn
w_Ti = - ky/kp * rhoLT
s_i = w / sqrt(2.)
b_i = (kx**2 + ky**2)
#electron
w_ne = ky/kp * rhoLn
w_Te = ky/kp * rhoLT
s_e = w / sqrt(2./mass_e)
b_e = (kx**2 + ky**2) * mass_e
# Plasma skin depth
delta = tau/(beta) / m_ie #sqrt(m_ie)
######################## Dispersion relation for gyrokinetic EM mode
# settings for the ions
Gamma_0i = Gamma0(b_i)
Gamma_1i = Gamma1(b_i)
Z_i = PlasmaDispersion(s_i)
l_i = 1. - (1. - w_ni / w) * Gamma_0i - w_Ti/w * (Gamma_0i - Gamma_1i ) * b_i
D_i = (1. - w_ni/w) * ( 1. + s_i * Z_i) * Gamma_0i + w_Ti/w * s_i * \
(0.5 * Z_i - s_i - s_i**2 * Z_i ) * Gamma_0i \
+ w_Ti/w * ( 1. + s_i * Z_i) * ( Gamma_0i - Gamma_1i) * b_i
# settings for the electrons
Gamma_0e = Gamma0(b_e)
Gamma_1e = Gamma1(b_e)
Z_e = PlasmaDispersion(s_e)
l_e = 1. - (1. - w_ne / w) * Gamma_0e - w_Te/w * (Gamma_0e - Gamma_1e ) * b_e
D_e = (1. - w_ne/w) * ( 1. + s_e * Z_e) * Gamma_0e + w_Te/w * s_e * \
(0.5 * Z_e - s_e - s_e**2 * Z_e ) * Gamma_0e \
+ w_Te/w * ( 1. + s_e * Z_e) * ( Gamma_0e - Gamma_1e) * b_e
#############################################################
# Standard Dispersion relation
if(mode == "EM"):
d = k_ortho2 * delta**2 * (l_i * tau + l_e + D_i * tau + D_e ) - 2 * s_e**2 * (D_i * tau + D_e) * (l_i * tau + l_e ) \
+ k_ortho2 * lambda_D**2 * ( k_ortho2 * delta**2 - 2 * s_e**2 * (D_i * tau + D_e))
# approximation for electrons
elif(mode == "ETG"):
d = 1. + l_e + D_e + lambda_D**2 * k_ortho2
# bad charge is wrong sign
elif(mode == "ITG"):
d = 1. + l_i + D_i + lambda_D**2 * k_ortho2
# simplified ITG dispersion relation
# approximation for electrons
elif(mode == "ITGe"):
d = l_e + D_e + tau * (l_i + D_i)
else:
raise NameError('No such Dispersion Relation')
return d
# Take care of extra pie due to normalization
if (mode == "EM"):
#init, solver = (-0.01 +.005j, -0.015 + 0.008j, 0.008 + 0.002j), 'muller'
init, solver = (-0.1 +.05j, -0.2 + 0.08j, -0.00 + 0.02j), 'muller'
if ky < 2.:
init, solver = ( 0.02 -.02j, 0.04 + 0.04j, 0.01 - 0.0j), 'muller'
else :
#goes init, solver = ( -0.4 - .012j, -0.1 - 0.03j, -0.2 - 0.012j), 'muller'
init, solver = ( -0.4 - .012j, -0.1 - 0.03j, -0.2 - 0.012j), 'muller'
else :
init, solver = (0.01 +.0026j, 0.02 + 0.03j, 0.015 + 0.01j), 'muller'
#init, solver = 0.01 + .03j, 'muller'
return getZero(DR_Smoly, init=init, solver=solver)
