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
print(" We assume this is a location behind the drive beam:")
# rb_max is calculated above
drb_dxi_nb = lbn_wake.calc_drb_dxi_no_beam(rb, rb_max)
print(" drb_dxi (no beam) = ", rs_sigfig(drb_dxi_nb,3), " [rad]")
print()
print("*******")
print("Calculate local axial longitudinal electric field...")
print(" We assume this is a location behind the drive beam:")
Ez_nb = lbn_wake.calc_Ez_on_axis_no_beam(n_pe, rb, rb_max)
print(" Ez (no beam) = ", rs_sigfig(Ez_nb*1.e-9,3), " [GV/m] (+ or -)")
print()
print("*******")
print("Calculate the halfwidth of the plasma bubble:")
xi_b = lbn_wake.calc_bubble_halfwidth(rb_max)
print(" xi_b = ", rs_sigfig(xi_b*1.e6,3), " [microns]")
print()
print("*******")
print("Calculate local bubble radius at arbitrary location...")
print(" Selected location is 'xi=ct-z' (positive):")
xi = 0.3*xi_b
print(" xi = ", rs_sigfig(xi*1.e6,3), " [microns]")
rb = lbn_wake.calc_local_bubble_radius(xi, rb_max)
print(" rb = ", rs_sigfig(rb*1.e6,3), " [microns]")
print()
print("*******")
print("Calculate bubble radius at location of maximum...")
print(" Selected location is 'xi=xi_b' (positive):")
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)