def calculate_all_NL_amplitudes():
# Import cutoff-derived composition information
cutoff_filename = 'D://Google Drive//Uni//PhD 2017//Josh PhD Share Folder//Thesis//Data_Plots//20130725_RBSP-A//pearl_times.txt'
cutoff_dict = epd.read_cutoff_file(cutoff_filename)
#plot_amplitudes_from_data(_time_start, _time_end, probe=_probe, pad=600)
time_start = _time_start
time_end = _time_end
probe = 'a'
pad = 0
plot_start = time_start - np.timedelta64(int(pad), 's')
plot_end = time_end + np.timedelta64(int(pad), 's')
time, mag, edens, cold_dens, hope_dens, hope_tpar, hope_tperp, hope_anis, L_vals =\
load_and_interpolate_plasma_params(
plot_start, plot_end, probe, nsec=None,
rbsp_path='E://DATA//RBSP//', HM_filter_mhz=50.0,
time_array=None, check_interp=False)
mag_time, pc1_mags, HM_mags, imf_time, IA, IF, IP, stime, sfreq, spower = \
load_EMIC_IMFs_and_dynspec(plot_start, plot_end)
# Specify color values for time
time0 = time[0].astype(np.int64)
time1 = time[-1].astype(np.int64)
norm = mpl.colors.LogNorm(vmin=time0, vmax=time1, clip=False)
mapper = cm.ScalarMappable(norm=norm, cmap=cm.jet)
lpad = 20
fig, axes = plt.subplots(nrows=4,
ncols=2,
figsize=(8.27, 11.69),
gridspec_kw={
'width_ratios': [1, 0.01],
'height_ratios': [1, 1, 0.5, 2]
})
# Spectra/IP
im0 = axes[0, 0].pcolormesh(stime,
sfreq,
spower.sum(axis=0).T,
cmap='jet',
norm=colors.LogNorm(vmin=1e-4, vmax=1e1))
axes[0, 0].set_ylim(0, fmax)
axes[0, 0].set_ylabel('$f$\n(Hz)', rotation=0, labelpad=lpad, fontsize=12)
fig.colorbar(im0, cax=axes[0, 1],
extend='both').set_label(r'$\frac{nT^2}{Hz}$',
fontsize=16,
rotation=0,
labelpad=5)
axes[0, 0].plot(imf_time, IF[0][:, 0], c='k', lw=0.75)
axes[0, 0].plot(imf_time, IF[1][:, 0], c='k', lw=0.75, alpha=0.8)
#axes[0, 0].plot(imf_time, IF[2][:, 0], c='k', lw=0.75, alpha=0.6)
#axes[0, 0].axvline(this_time, color='white', ls='-' , alpha=0.7)
axes[0, 0].set_xlim(plot_start, plot_end)
axes[0, 0].set_xticklabels([])
axes[0, 0].axhline(_band_start, color='white', ls='--')
axes[0, 0].axhline(_band_end, color='white', ls='--')
# mag_time, pc1_mags, IA, IF, IP, stime, sfreq, spower
# Timeseries for comparison
axes[1, 0].plot(mag_time, pc1_mags[:, 0], c='b', label='$\delta B_\\nu$')
axes[1, 0].plot(mag_time,
pc1_mags[:, 1],
c='r',
label='$\delta B_\phi$',
alpha=0.5)
#axes[1, 0].plot(mag_time, pc1_mags[:, 2], c='k', label='$\delta B_\mu$', alpha=0.25)
axes[1, 0].set_ylabel('nT', rotation=0, labelpad=lpad)
axes[1, 0].set_xlim(plot_start, plot_end)
axes[1, 0].set_xlabel('Time [UT]')
axes[1, 0].set_xlim(plot_start, plot_end)
# CALCULATE PLASMA PARAMETERS AND AMPLITUDES FOR ALL TIMES
# Plot all on same graph, use colorbar to discern time
# Maybe do for cutoff times/packet times
for ii in range(0, time.shape[0], 4):
this_time = time[ii]
clr = mapper.to_rgba(time[ii].astype(np.int64))
print('Doing time:', this_time)
# Get oxygen concentration from cutoffs
cutoff = np.interp(this_time.astype(np.int64),
cutoff_dict['CUTOFF_TIME'].astype(np.int64),
cutoff_dict['CUTOFF_NORM'])
o_frac = epd.calculate_o_from_he_and_cutoff(cutoff, he_frac)
h_frac = 1. - he_frac - o_frac
# Cold plasma params, SI units
B0 = mag[ii]
name = np.array(['H', 'He', 'O'])
mass = np.array([1.0, 4.0, 16.0]) * PMASS
charge = np.array([1.0, 1.0, 1.0]) * PCHARGE
density = np.array([h_frac, he_frac, o_frac]) * edens[ii]
ani = np.array([0.0, 0.0, 0.0])
tpar = np.array([0.0, 0.0, 0.0])
tper = (ani + 1) * tpar
Species, PP = create_species_array(B0, name, mass, charge, density,
tper, ani)
# Frequencies to evaluate, calculate wavenumber (cold approximation)
f_min = 0.07 * PP['pcyc_rad'] / (2 * np.pi)
f_max = 0.24 * PP['pcyc_rad'] / (2 * np.pi)
Nf = 10000
f_vals = np.linspace(f_min, f_max, Nf)
w_vals = 2 * np.pi * f_vals
k_vals = nls.get_k_cold(w_vals, Species)
# Define hot proton parameters (velocities normalized c)
# Remember: temperatures originally in eV
nh = hope_dens[0][ii]
wph2 = nh * PCHARGE**2 / (PMASS * EPS0)
Vth_para = np.sqrt(KB * hope_tpar[0][ii] *
(PCHARGE / KB) / PMASS) / SPLIGHT
Vth_perp = np.sqrt(KB * hope_tperp[0][ii] *
(PCHARGE / KB) / PMASS) / SPLIGHT
Q = 0.5
# Curvature parameters (this has the most wiggle room)
L = 4.7 #L_vals[ii]
a = 4.5 / (L * RE)**2
a = a * (SPLIGHT**2 / PP['pcyc_rad']**2)
Vg, Vp, Vr = nls.get_velocities(w_vals, Species, PP, normalize=True)
s0, s1, s2 = nls.get_inhomogeneity_terms(w_vals,
Species,
PP,
Vth_perp,
normalize_vel=True)
# Normalize input parameters
wph = np.sqrt(wph2) / PP['pcyc_rad']
w = w_vals / PP['pcyc_rad']
# DO THE ACTUAL CALCULATION (All hands off from here, using existing code/proforma)
tau = 1.00
B_th = nls.get_threshold_amplitude(w, wph, Q, s2, a, Vp, Vr, Vth_para,
Vth_perp)
B_opt = nls.get_optimum_amplitude(w, wph, Q, tau, s0, s1, Vg, Vr,
Vth_para, Vth_perp)
T_tr = nls.get_nonlinear_trapping_period(k_vals, Vth_perp * SPLIGHT,
B_opt * PP['B0'])
T_N = tau * T_tr * PP['pcyc_rad']
# Filter zeros and infs:
B_th[B_th == np.inf] = np.nan
B_th[B_th == 0] = np.nan
B_opt[B_opt == np.inf] = np.nan
B_opt[B_opt == 0] = np.nan
T_N[T_N == np.inf] = np.nan
T_N[T_N == 0] = np.nan
################
### PLOTTING ###
################
# Bth, Bopt, Inst. Amplitudes
axes[3, 0].plot(f_vals,
B_th * B0 * 1e9,
c=clr,
ls='--',
label=r'$B_{th}$')
axes[3, 0].plot(f_vals,
B_opt * B0 * 1e9,
c=clr,
ls='-',
label=r'$B_{opt}$')
axes[3, 0].set_ylabel('$B$ [nT]', rotation=0, labelpad=20, fontsize=16)
axes[3, 0].set_xlabel('$f$ [Hz]', fontsize=16)
axes[3, 0].set_ylim(0, 17)
axes[3, 0].set_xlim(f_vals[0], f_vals[-1])
axes[3, 0].tick_params(top=True, right=True)
add_custom_legend(axes[3, 0], [r'$B_{th}$', r'$B_{opt}$'], ['--', '-'],
[1.0, 1.0], ['k', 'k'])
label_every = 15
cbar = fig.colorbar(mapper,
cax=axes[3, 1],
label='Time',
orientation='vertical',
ticks=time[::label_every].astype(np.int64))
for label in cbar.ax.get_yminorticklabels():
label.set_visible(False)
cbar.ax.set_yticklabels(time[::label_every].astype('datetime64[m]'))
axes[1, 1].set_visible(False)
axes[2, 0].set_visible(False)
axes[2, 1].set_visible(False)
axes[0, 0].xaxis.set_major_formatter(mdates.DateFormatter('%H:%M:%S'))
axes[1, 0].xaxis.set_major_formatter(mdates.DateFormatter('%H:%M:%S'))
fig.tight_layout()
fig.subplots_adjust(wspace=0.05, hspace=0)
fig.align_ylabels()
plt.show()
return
# Define hot proton parameters (velocities normalized c) : vth = sqrt(kT/m)?
# Remember: temperatures originally in eV
nh = hope_dens[0][time_idx]
wph2 = nh * PCHARGE**2 / (PMASS * EPS0)
Vth_para = np.sqrt(KB * hope_tpar[0][time_idx] *
(PCHARGE / KB) / PMASS) / SPLIGHT
Vth_perp = np.sqrt(KB * hope_tperp[0][time_idx] *
(PCHARGE / KB) / PMASS) / SPLIGHT
Q = 0.5
# Curvature parameters (this has the most wiggle room)
a = 4.5 / (L * RE)**2
a = a * (SPLIGHT**2 / PP['pcyc_rad']**2)
Vg, Vp, Vr = nls.get_velocities(w_vals,
Species,
PP,
normalize=True)
s0, s1, s2 = nls.get_inhomogeneity_terms(w_vals,
Species,
PP,
Vth_perp,
normalize_vel=True)
# Normalize input parameters
wph = np.sqrt(wph2) / PP['pcyc_rad']
w = w_vals / PP['pcyc_rad']
# DO THE ACTUAL CALCULATION (All hands off from here, using existing code/proforma)
tau = 1.00
B_th = nls.get_threshold_amplitude(w, wph, Q, s2, a, Vp, Vr,
Vth_para, Vth_perp)
# Cold plasma params, SI units
B0 = mag[ii]
name = np.array(['H' , 'He' , 'O' ])
mass = np.array([1.0 , 4.0 , 16.0 ]) * PMASS
charge = np.array([1.0 , 1.0 , 1.0 ]) * PCHARGE
density = np.array([h_frac, he_frac, o_frac[ii] ]) * edens[ii]
ani = np.array([0.0 , 0.0 , 0.0 ])
tpar = np.array([0.0 , 0.0 , 0.0 ])
tper = (ani + 1) * tpar
Species, PP = create_species_array(B0, name, mass, charge, density, tper, ani)
# Velocities and Energies
k_vals = nls.get_k_cold(w_vals, Species)
all_VG[ii], all_VP[ii], all_VR[ii] = nls.get_velocities(w_vals, Species, PP)
all_LR[ii], all_CR[ii] = nls.get_energies(w_vals, k_vals, PP['pcyc_rad'], PMASS)
fidx = np.where(abs(f_vals - max_freqs[ii]) == np.min(abs(f_vals - max_freqs[ii])))[0][0]
freq = f_vals[fidx]
# Get values at the frequency of max power
line_LR[ii] = all_LR[ii, fidx]
line_CR[ii] = all_CR[ii, fidx]
line_VP[ii] = all_VP[ii, fidx]
line_VG[ii] = all_VG[ii, fidx]
line_VR[ii] = all_VR[ii, fidx]
# Line plots for each he_frac
axes[1, 0].plot(time, line_CR*1e-3, c=clr, lw=0.75, label=f'{he_frac*100.:.0f}% $He^+$')
def plot_velocities_and_energies_single(time_start, time_end, probe='a'):
# Import cutoff-derived composition information
cutoff_dict = epd.read_cutoff_file(cutoff_filename)
# Load particle and field information
time, mag, edens = load_CRRES_data(time_start, time_end, nsec=None,
crres_path='E://DATA//CRRES//')
mag_time, pc1_mags, HM_mags, imf_time, IA, IF, IP, stime, sfreq, spower = \
load_EMIC_IMFs_and_dynspec(time_start, time_end)
spower = spower.sum(axis=0)
cutoff = np.interp(time.astype(np.int64),
cutoff_dict['CUTOFF_TIME'].astype(np.int64),
cutoff_dict['CUTOFF_NORM'])
o_fracs = epd.calculate_o_from_he_and_cutoff(cutoff, he_frac)
# Get velocity/energy data for time
plt.ioff()
for ii in range(time.shape[0]):
# Define time, time index
this_time = time[ii]
maxpwr_tidx = np.where(abs(stime - this_time) == np.min(abs(stime - this_time)))[0][0]
# Find max freq and index
fst, fen = ascr.boundary_idx64(sfreq, _band_start, _band_end)
maxpwr_fidx = spower[maxpwr_tidx, fst:fen].argmax()
maxpwr_fidx += fst
maxpwr_freq = sfreq[maxpwr_fidx]
#date_string = this_time.astype(object).strftime('%Y%m%d')
save_string = this_time.astype(object).strftime('%Y%m%d_%H%M%S')
#clr = mapper.to_rgba(time[ii].astype(np.int64))
print('Doing time:', this_time)
fig, axes = plt.subplots(nrows=4, ncols=2, figsize=(8.0, 0.5*11.00),
gridspec_kw={'width_ratios':[1, 0.01],
'height_ratios':[1, 2, 2, 2]
})
# Spectra/IP
im0 = axes[0, 0].pcolormesh(stime, sfreq, spower.T, cmap='jet',
norm=colors.LogNorm(vmin=1e-4, vmax=1e1))
axes[0, 0].set_ylim(0, _band_end)
axes[0, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im0, cax=axes[0, 1], extend='both').set_label(
r'$\frac{nT^2}{Hz}$', fontsize=16, rotation=0, labelpad=15)
axes[0, 0].axvline(this_time, color='white', ls='-' , alpha=0.7)
axes[0, 0].set_xlim(time_start, time_end)
axes[0, 0].set_xticklabels([])
axes[0, 0].axvline(this_time, color='white', ls='-', alpha=0.75)
axes[0, 0].axhline(maxpwr_freq, color='white', ls='-', alpha=0.75)
axes[0, 0].set_title(f'Velocities and Energies :: {this_time}')
h_frac = 1. - he_frac - o_fracs[ii]
# Cold plasma params, SI units
B0 = mag[ii]
name = np.array(['H' , 'He' , 'O' ])
mass = np.array([1.0 , 4.0 , 16.0 ]) * PMASS
charge = np.array([1.0 , 1.0 , 1.0 ]) * PCHARGE
density = np.array([h_frac, he_frac, o_fracs[ii] ]) * edens[ii]
ani = np.array([0.0 , 0.0 , 0.0 ])
tpar = np.array([0.0 , 0.0 , 0.0 ])
tper = (ani + 1) * tpar
Species, PP = create_species_array(B0, name, mass, charge, density, tper, ani)
# Frequencies to evaluate, calculate wavenumber (cold approximation)
f_min = _band_start
f_max = _band_end
Nf = 10000
f_vals = np.linspace(f_min, f_max, Nf)
w_vals = 2*np.pi*f_vals
k_vals = nls.get_k_cold(w_vals, Species)
wv_len = 1e-3 * 2*np.pi / k_vals
fidx = np.where(abs(f_vals - maxpwr_freq) == np.min(abs(f_vals - maxpwr_freq)))[0][0]
freq = f_vals[fidx]
axes[1, 0].plot(f_vals, wv_len, c='k')
axes[1, 0].set_ylabel('$\lambda_{EMIC}$ [km]')
axes[1, 0].set_ylim(0, 2000)
# Velocities
Vg, Vp, Vr = nls.get_velocities(w_vals, Species, PP)
axes[2, 0].semilogy(f_vals, Vg*1e-3, c='k', label='$V_g$')
axes[2, 0].semilogy(f_vals, Vp*1e-3, c='r', label='$V_p$')
axes[2, 0].semilogy(f_vals,-Vr*1e-3, c='b', label='$-V_R$')
axes[2, 0].set_ylim(10, 4500)
axes[2, 0].set_ylabel('Velocities [km/s]')
axes[2, 0].legend(bbox_to_anchor=(1.0, 0), loc=3, borderaxespad=0.)
# Energies
ELAND, ECYCL = nls.get_energies(w_vals, k_vals, PP['pcyc_rad'], PMASS)
axes[3, 0].semilogy(f_vals, ELAND*1e-3, c='r', label='$E_0$')
axes[3, 0].semilogy(f_vals, ECYCL*1e-3, c='b', label='$E_1$')
axes[3, 0].set_ylim(1e-1, 1e3)
axes[3, 0].set_ylabel('$E_R$ [keV]')
axes[3, 0].set_xlabel('Freq [Hz]', rotation=0)
axes[3, 0].legend(bbox_to_anchor=(1.0, 0), loc=3, borderaxespad=0.)
# Work out what the energy is at maxpwr_freq
num_landau = ELAND[fidx]*1e-3
num_cyclotron = ECYCL[fidx]*1e-3
axes[3, 0].text(0.8, 0.9, f'$E_0(f) =$ {num_landau:.1f} keV', horizontalalignment='left',
verticalalignment='center', transform=axes[3, 0].transAxes)
axes[3, 0].text(0.8, 0.8, f'$E_1(f) =$ {num_cyclotron:.1f} keV', horizontalalignment='left',
verticalalignment='center', transform=axes[3, 0].transAxes)
axes[0, 0].set_xticklabels([])
axes[1, 0].set_yticks(np.array([0, 500, 1000, 1500]))
for ax in axes[1:, 0]:
ax.set_xlim(_band_start, _band_end)
ax.axvline(freq, color='k', alpha=0.5, ls='--')
if ax != axes[-1, 0]:
ax.set_xticklabels([])
axes[1, 1].set_visible(False)
axes[2, 1].set_visible(False)
axes[3, 1].set_visible(False)
#fig.tight_layout(rect=[0, 0, 0.95, 1])
fig.tight_layout()
fig.subplots_adjust(wspace=0.05, hspace=0)
fig.align_ylabels()
if save_plot == True:
print('Saving plot...')
fig.savefig(_plot_path + 'VELENG_FROMDATA_' + save_string + '.png', dpi=dpi)
plt.close('all')
else:
plt.show()
return
def plot_HM_and_energy(time_start, time_end, probe):
'''
For a specific frequency, calculate what the first order cyclotron resonance
energy is and plot this as a timeseries. Secondary plots for the Pc1 spectra
and HM/|B| spectra
Do for all frequencies and select specific frequency at end (or option to
show as a pcolormesh)
'''
# Import cutoff-derived composition information
cutoff_filename = 'D://Google Drive//Uni//PhD 2017//Josh PhD Share Folder//Thesis//Data_Plots//20130725_RBSP-A//pearl_times.txt'
cutoff_dict = epd.read_cutoff_file(cutoff_filename)
time, mag, edens, cold_dens, hope_dens, hope_tpar, hope_tperp, hope_anis, L_vals =\
load_and_interpolate_plasma_params(
time_start, time_end, probe, nsec=None,
rbsp_path='E://DATA//RBSP//', HM_filter_mhz=50.0,
time_array=None, check_interp=False)
mag_time, pc1_mags, HM_mags, imf_time, IA, IF, IP, stime, sfreq, spower = \
load_EMIC_IMFs_and_dynspec(time_start, time_end)
# Frequencies to evaluate, calculate wavenumber (cold approximation)
f_min = _band_start
f_max = _band_end
Nf = 10000
f_vals = np.linspace(f_min, f_max, Nf)
w_vals = 2 * np.pi * f_vals
all_CR = np.zeros((time.shape[0], Nf), dtype=np.float64)
all_LR = np.zeros((time.shape[0], Nf), dtype=np.float64)
all_VP = np.zeros((time.shape[0], Nf), dtype=np.float64)
all_VG = np.zeros((time.shape[0], Nf), dtype=np.float64)
all_VR = np.zeros((time.shape[0], Nf), dtype=np.float64)
# Collect info for each time
for ii in range(time.shape[0]):
this_time = time[ii]
print('Doing time:', this_time)
# Get oxygen concentration from cutoffs
cutoff = np.interp(this_time.astype(np.int64),
cutoff_dict['CUTOFF_TIME'].astype(np.int64),
cutoff_dict['CUTOFF_NORM'])
o_frac = epd.calculate_o_from_he_and_cutoff(cutoff, he_frac)
h_frac = 1. - he_frac - o_frac
# Cold plasma params, SI units
B0 = mag[ii]
name = np.array(['H', 'He', 'O'])
mass = np.array([1.0, 4.0, 16.0]) * PMASS
charge = np.array([1.0, 1.0, 1.0]) * PCHARGE
density = np.array([h_frac, he_frac, o_frac]) * edens[ii]
ani = np.array([0.0, 0.0, 0.0])
tpar = np.array([0.0, 0.0, 0.0])
tper = (ani + 1) * tpar
Species, PP = create_species_array(B0, name, mass, charge, density,
tper, ani)
# Velocities and Energies
k_vals = nls.get_k_cold(w_vals, Species)
all_VG[ii], all_VP[ii], all_VR[ii] = nls.get_velocities(
w_vals, Species, PP)
all_LR[ii], all_CR[ii] = nls.get_energies(w_vals, k_vals,
PP['pcyc_rad'], PMASS)
fig, axes = plt.subplots(nrows=5,
ncols=2,
figsize=(8.0, 1.0 * 11.00),
gridspec_kw={'width_ratios': [1, 0.01]})
# To plot: Spectra, velocities (Vg, Vr) and energies (cyclotron, landau resonances)
# HM/|B| overlay
with warnings.catch_warnings():
warnings.simplefilter("ignore")
axes[0, 0].set_title(f'Velocities and Energies :: {this_time}')
# Spectra
im0 = axes[0, 0].pcolormesh(stime,
sfreq,
spower.sum(axis=0).T,
cmap='jet',
norm=colors.LogNorm(vmin=1e-4, vmax=1e1))
axes[0, 0].set_ylim(0, fmax)
axes[0, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im0, cax=axes[0, 1],
extend='both').set_label(r'$\frac{nT^2}{Hz}$',
fontsize=14,
rotation=0,
labelpad=15)
# E_RES_CYCLOTRON
im1 = axes[1, 0].pcolormesh(time,
f_vals,
all_CR.T * 1e-3,
cmap='jet',
norm=colors.Normalize())
axes[1, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im1, cax=axes[1, 1],
extend='both').set_label('$E_R$ Cyclotron\n[keV]',
fontsize=14,
rotation=0,
labelpad=15)
# E_RES_LANDAU
im2 = axes[2, 0].pcolormesh(time,
f_vals,
all_LR.T * 1e-3,
cmap='jet',
norm=colors.Normalize())
axes[2, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im2, cax=axes[2, 1],
extend='both').set_label('$E_R$ Landau\n[keV]',
fontsize=14,
rotation=0,
labelpad=15)
# VR
im3 = axes[3, 0].pcolormesh(time,
f_vals,
all_VR.T * 1e-3,
cmap='jet',
norm=colors.Normalize())
axes[3, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im3, cax=axes[3, 1],
extend='both').set_label('$V_R$\n[$km/s$]',
fontsize=14,
rotation=0,
labelpad=15)
# VG
im4 = axes[4, 0].pcolormesh(time,
f_vals,
all_VG.T * 1e-3,
cmap='jet',
norm=colors.Normalize())
axes[4, 0].set_ylabel('$f$ [Hz]', rotation=90)
fig.colorbar(im4, cax=axes[4, 1],
extend='both').set_label('$V_G$\n[$km/s$]',
fontsize=14,
rotation=0,
labelpad=15)
for ax in axes[:, 0]:
ax.set_xlim(time_start, time_end)
ax.set_ylim(_band_start, _band_end)
ax2 = ax.twinx()
ax2.plot(mag_time, HM_mags[:, 2], c='k', lw=0.75)
fig.tight_layout()
fig.subplots_adjust(wspace=0.05, hspace=0)
fig.align_ylabels()
if save_plot == True:
save_string = time_start.astype(object).strftime('%Y%m%d_%H%M')
print('Saving plot...')
fig.savefig(_plot_path + 'VELENG_FROMDATA_PCOLOR_' + save_string +
'.png')
plt.close('all')
else:
plt.show()
return