def plot_theory(v0, mass_ratio):
alpha = np.linspace(0, 5, num=200)
if v0 > 5.0:
print('v0 should be <= 5.0')
return
#rmass=1.0/100.0
rmass = mass_ratio
#v0=3.0
growth_rate = osiris.buneman_growth_rate(alpha, rmass)
growth_rate_func = interp1d(alpha, np.abs(growth_rate), kind='cubic')
karray = np.arange(0.01, 1.0, 0.01)
nk = 49
growth_rate = np.zeros(nk)
growth_rate = growth_rate_func(karray * v0)
maxgr = max(growth_rate)
print("Max growth rate is {:.3f}, occurring at k = {:.2f}".format(
maxgr, karray[np.argmax(growth_rate)]))
print("Instability edge is at k = {:.2f}".format(
karray[np.where(growth_rate < 0.001)[0]][0]))
plt.figure(figsize=(8, 5))
plt.plot(karray,
growth_rate,
label='Theory: $v_0 = ' + repr(v0) + '$,\n' +
'mass ratio $m/M = ' + repr(rmass) + '$')
plt.xlabel('Wavenumber [$1/\Delta x$]', **axis_font)
plt.ylabel('Growth Rate [$\omega_{pe}$]', **axis_font)
plt.legend()
plt.show()
def plot_theory(v0=10.0, density_ratio=1 / 100):
alpha = np.linspace(0, 20, num=200)
rmass = density_ratio
growth_rate = osiris.buneman_growth_rate(alpha, rmass)
growth_rate_func = interp1d(alpha, np.abs(growth_rate), kind='cubic')
#v0=10.0
c = rmass
karray = np.arange(0.0005, 1, 0.005)
nk = 49
growth_rate = np.zeros(nk)
growth_rate = growth_rate_func(karray * v0)
plt.figure(figsize=(8, 5))
plt.plot(karray,
growth_rate,
label='Theory: $v_0 = ' + repr(v0) + '$,\n' +
'den ratio $n_b/n_0 = ' + repr(c) + '$')
plt.xlabel('Wavenumber [$1/\Delta x$]', **axis_font)
plt.ylabel('Growth Rate [$\omega_{pe}$]', **axis_font)
plt.legend()
plt.show()
def get_theory(v0, mass_ratio):
alpha = np.linspace(0, 5, num=200)
if v0 > 5.0:
print('v0 should be <= 5.0')
return
#rmass=1.0/100.0
rmass = mass_ratio
#v0=3.0
growth_rate = osiris.buneman_growth_rate(alpha, rmass)
growth_rate_func = interp1d(alpha, np.abs(growth_rate), kind='cubic')
karray = np.arange(0.01, 1.0, 0.01)
nk = 49
growth_rate = np.zeros(nk)
growth_rate = growth_rate_func(karray * v0)
maxgr = max(growth_rate)
return maxgr, karray[np.argmax(growth_rate)], karray[np.where(
growth_rate < 0.001)[0]][0]
def compare_sim_with_theory(output_directory, v0, mode, mass_ratio):
alpha = np.arange(0, 2.0, 0.01)
rmass = mass_ratio
growth_rate = osiris.buneman_growth_rate(alpha, rmass)
growth_rate_func = interp1d(alpha, np.abs(growth_rate), kind='cubic')
workdir = os.getcwd()
dirname = output_directory
filename = workdir + '/' + dirname + '/Ex.h5'
test4 = h5_utilities.read_hdf(filename)
k_data = np.fft.fft(test4.data, axis=1)
test4.data = np.abs(k_data)
test4.axes[0].axis_max = 2.0 * 3.1415926
nx = test4.data.shape[1]
nt = test4.data.shape[0]
dk = 2 * 3.1415926 / nx
display_mode = mode
bracket = False
#v0=3.0
alpha = v0 * dk * (display_mode)
# growth_rate = 0.0
# if (alpha<np.sqrt(2)):
growth_rate = growth_rate_func(alpha)[()]
taxis = np.linspace(0, test4.axes[1].axis_max, nt)
stream_theory = np.zeros(nt)
stream_theory_plus = np.zeros(nt)
stream_theory_minus = np.zeros(nt)
init_amplitude = 1e-7
for it in range(0, nt):
stream_theory[it] = init_amplitude * np.exp(growth_rate * taxis[it])
stream_theory_plus[it] = init_amplitude * np.exp(
1.15 * growth_rate * taxis[it])
stream_theory_minus[it] = init_amplitude * np.exp(
0.85 * growth_rate * taxis[it])
plt.figure(figsize=(8, 6))
plt.semilogy(taxis,
test4.data[:, display_mode],
label='PIC simulation, mode =' + repr(display_mode))
plt.semilogy(taxis,
stream_theory,
'r',
label='theory, growth rate =' + '%.3f' % growth_rate)
if (bracket):
plt.semilogy(taxis, stream_theory_plus, 'g.')
plt.semilogy(taxis, stream_theory_minus, 'g.')
plt.ylim((1e-7, 1000))
plt.legend()
plt.xlabel('Time $[1/\omega_{pe}]$', **axis_font)
plt.ylabel('Time History [a.u.]', **axis_font)
plt.show()
def compare_sim_with_theory(output_directory, v0, mode, density_ratio):
alpha = np.linspace(0, 20, num=200)
rmass = density_ratio
growth_rate = osiris.buneman_growth_rate(alpha, rmass)
growth_rate_func = interp1d(alpha, np.abs(growth_rate), kind='cubic')
workdir = os.getcwd()
dirname = output_directory
filename = workdir + '/' + dirname + '/Ex.h5'
# print(filename)
test4 = h5_utilities.read_hdf(filename)
# here we fourier analyze the data in space
#
# k_data=np.fft.fft(test.data,axis=1)
k_data = np.fft.fft(test4.data, axis=1)
# k_data_2=np.fft.fft(k_data,axis=0)
test4.data = np.abs(k_data)
test4.axes[0].axis_max = 2.0 * 3.1415926
nx = test4.data.shape[1]
nt = test4.data.shape[0]
# print(repr(nt))
dk = 2 * 3.1415926 / nx
# print('Delta k = '+repr(dk))
# To compare with theory, just specify the mode you want to look at here
#
display_mode = mode
bracket = False
#
#
#v0=10.0
alpha = v0 * dk * (display_mode)
# growth_rate = 0.0
# if (alpha<np.sqrt(2)):
growth_rate = growth_rate_func(alpha)[()]
taxis = np.linspace(0, test4.axes[1].axis_max, nt)
stream_theory = np.zeros(nt)
stream_theory_plus = np.zeros(nt)
stream_theory_minus = np.zeros(nt)
init_amplitude = 1e-7
for it in range(0, nt):
stream_theory[it] = init_amplitude * np.exp(growth_rate * taxis[it])
stream_theory_plus[it] = init_amplitude * np.exp(
1.15 * growth_rate * taxis[it])
stream_theory_minus[it] = init_amplitude * np.exp(
0.85 * growth_rate * taxis[it])
plt.figure(figsize=(8, 5))
plt.semilogy(taxis,
test4.data[:, display_mode],
label='PIC simulation, mode =' + repr(display_mode))
plt.semilogy(taxis,
stream_theory,
'r',
label='theory, growth rate =' + '%.3f' % growth_rate)
if (bracket):
plt.semilogy(taxis, stream_theory_plus, 'g.')
plt.semilogy(taxis, stream_theory_minus, 'g.')
plt.ylim((1e-7, 1000))
plt.legend()
plt.xlabel('Time $[1/\omega_{pe}]$', **axis_font)
plt.ylabel('Mode amplitude [a.u.]', **axis_font)
plt.show()