def plot_Ez_on_axis(n_pe, beam_tot_z, beam_num_ptcl):
"""
Plot the longitudinal electric field in a plasma bubble.
Valid in "strong bubble regime", where rb_max*k_pe >> 1.
Args:
n_pe: number density of the electron plasma
beam_tot_z: total length of the drive beam
beam_num_ptcl: number of e- in the drive beam
Returns:
ax: matplotlib 'Axis' object for Ez inside bubble
"""
# calculate the maximum bubble radius
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
# calculate the bubble half width
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
# calculate the approximate (constant?) decelerating field
# along the drive beam
E_decel = lbn_wake.calc_E_decel_along_beam(n_pe, beam_tot_z, beam_num_ptcl)
# Specify the plot range, xi_min <= xi <= xi_max
# xi=ct-z is the distance from the front of the bubble (positive)
xi_min = 0.
xi_max = 1.99 * xi_b
num_points = 100
xi_array = np.linspace(xi_min, xi_max, num=num_points)
ez_array = np.zeros(num_points)
for iloop in range(0, num_points):
xi = xi_array[iloop]
if xi < 0. or xi > 2. * xi_b: ez_array[iloop] = 0.
elif xi < beam_tot_z: ez_array[iloop] = E_decel
else:
rb = lbn_wake.calc_local_bubble_radius(xi, rb_max)
ez_array[iloop] = lbn_wake.calc_Ez_on_axis_no_beam(
n_pe, rb, rb_max)
# normalize units to GV/m and microns
ez_array *= 1.e-9
xi_array *= 1.e6
# generate the plot
ax = plt.subplot(111)
ax.plot(xi_array, ez_array)
ax.set_xlabel('xi = ct - z [microns]')
ax.set_ylabel('(axial) Ez [GV/m]')
ax.set_title('PWFA axial Ez in "strong" regime')
return ax
def plot_bubble_radius(n_pe, beam_tot_z, beam_num_ptcl):
"""
Plot the plasma bubble radius.
Valid in "strong bubble regime", where rb_max*k_pe >> 1.
Args:
n_pe: number density of the electron plasma
beam_tot_z: total length of the drive beam
beam_num_ptcl: number of e- in the drive beam
Returns:
ax: matplotlib 'Axis' object for bubble radius plot
"""
# calculate the maximum bubble radius
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
# calculate the bubble half width
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
# Specify the plot range, xi_min <= xi <= xi_max
# xi=ct-z is the distance from the front of the bubble (positive)
xi_min = 0.
xi_max = 2. * xi_b
num_points = 200
xi_array = np.linspace(xi_min, xi_max, num=num_points)
rb_array = np.zeros(num_points)
for iloop in range(0, num_points):
rb_array[iloop] = lbn_wake.calc_local_bubble_radius(
xi_array[iloop], rb_max)
# normalize units to microns
rb_array *= 1.e6
xi_array *= 1.e6
# generate the plot
ax = plt.subplot(111)
ax.plot(xi_array, rb_array)
ax.set_xlabel('xi = ct - z [microns]')
ax.set_ylabel('rb [microns]')
ax.set_title('PWFA bubble radius in "strong" regime')
return ax
# The accelerated "witness" beam, also assumed Gaussian
# -------------------
wb_rms_r = 0.012 * lambda_pe # [m] RMS radius
wb_rms_z = 0.036 * lambda_pe # [m] RMS length
wb_tot_q = 0.100e-9 # [C] total charge of 100 pC
wb_gamma = 100 # relativistic gamma factor
wb_trail = 0.900 * lambda_pe # [m] trailing distance behind center of drive beam
# -----------------
# Excercise some of the methods
#------------------
print()
print("*******")
print("Calculate the maximum radius of the plasma bubble:")
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
print(" rb_max = ", rs_sigfig(rb_max*1.e6,3), " [microns]")
print()
print("*******")
print("Calculate the 1st 'strong bubble' validity condition...")
print("(bubble radius) / (plasma skin depth); it must be large:")
strong_check_1 = rb_max*k_pe
print(" 1st validity ratio = ", rs_sigfig(strong_check_1,3))
print()
print("*******")
print("Calculate the 2nd 'strong bubble' validity condition...")
print("(scaled beam dens) / (plasma dens); it must be large:")
strong_check_2 = beam_num_ptcl/n_pe/beam_tot_z**3
print(" 2nd validity ratio = ", rs_sigfig(strong_check_2,3))
def test_lbn_07():
rb = 0.4 * lambda_pe
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
Ez_nb = lbn_wake.calc_Ez_on_axis_no_beam(n_pe, rb, rb_max)
assert rs_sigfig(Ez_nb * 1.e-9, 3) == rs_sigfig(-31.9, 3)
def test_lbn_06():
rb = 0.4 * lambda_pe
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
drb_dxi_nb = lbn_wake.calc_drb_dxi_no_beam(rb, rb_max)
assert rs_sigfig(drb_dxi_nb, 3) == rs_sigfig(1.32, 3)
def test_lbn_04():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
p_beam_plasma = lbn_wake.calc_power_beam_plasma(n_pe, rb_max)
assert rs_sigfig(p_beam_plasma, 3) == rs_sigfig(2.19e+20, 3)
def test_lbn_02():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
strong_check_1 = rb_max * k_pe
assert rs_sigfig(strong_check_1, 3) == rs_sigfig(3.66, 3)
def test_lbn_01():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
assert rs_sigfig(rb_max * 1.e6, 3) == rs_sigfig(97.2, 3)
def test_lbn_10():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
rb = lbn_wake.calc_local_bubble_radius(xi_b, rb_max)
assert rs_sigfig(rb * 1.e6, 3) == rs_sigfig(97.2, 3)
def test_lbn_09():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
xi = 0.3 * xi_b
rb = lbn_wake.calc_local_bubble_radius(xi, rb_max)
assert rs_sigfig(rb * 1.e6, 3) == rs_sigfig(77.7, 3)
def test_lbn_08():
rb_max = lbn_wake.calc_rb_max(n_pe, beam_tot_z, beam_num_ptcl)
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
assert rs_sigfig(xi_b * 1.e6, 3) == rs_sigfig(82.3, 3)
