Plasma beamline simulation

This tutorial illustrates how to carry out a simulation of a multi-element plasma-acceleration beamline.

The setup considered is an LPA with external injection followed by an active plasma lens for beam capturing.

Create particle bunch

from wake_t.utilities.bunch_generation import get_gaussian_bunch_from_size

# Beam parameters.
emitt_nx = emitt_ny = 1e-6  # m
s_x = s_y = 3e-6  # m
s_t = 3.0  # fs
gamma_avg = 100 / 0.511
gamma_spread = 1.0  # %
q_bunch = 30  # pC
xi_avg = 0.0  # m
n_part = 1e4

# Create particle bunch.
bunch = get_gaussian_bunch_from_size(
    emitt_nx,
    emitt_ny,
    s_x,
    s_y,
    gamma_avg,
    gamma_spread,
    s_t,
    xi_avg,
    q_bunch,
    n_part,
    name="elec_bunch",
)

# Show phase space.
bunch.show()

Create laser driver

from wake_t import GaussianPulse

# Laser parameters.
laser_xi_c = 60e-6  # m (laser centroid in simulation box)
w_0 = 40e-6  # m
a_0 = 3
tau = 30e-15  # fs (FWHM in intensity)
z_foc = 1e-2  # laser focus at center of LPA.

# Create Gaussian laser pulse.
laser = GaussianPulse(laser_xi_c, w_0=w_0, a_0=a_0, tau=tau, z_foc=z_foc)

Create LPA

from wake_t import PlasmaStage

plasma_target = PlasmaStage(
    length=2e-2,
    density=1e23,
    wakefield_model="quasistatic_2d",
    xi_max=90e-6,
    xi_min=-40e-6,
    r_max=200e-6,
    n_xi=260,
    n_r=200,
    ppc=4,
    laser=laser,
    n_out=10,
)

Create beam capture section

from wake_t import Drift, ActivePlasmaLens

drift_1 = Drift(length=0.1, n_out=10)
drift_2 = Drift(length=0.1, n_out=10)

apl = ActivePlasmaLens(length=2e-2, foc_strength=400, wakefields=False, n_out=5)

Make beamline

from wake_t import Beamline

beamline = Beamline([plasma_target, drift_1, apl, drift_2])

Track bunch

bunch_list = beamline.track(bunch)

Plasma stage:   0%|          | 0.000000/0.020000 m [00:00]
Plasma stage:   3%|▎         | 0.000519/0.020000 m [00:00]
Plasma stage:   6%|▌         | 0.001169/0.020000 m [00:00]
Plasma stage:   9%|▉         | 0.001818/0.020000 m [00:00]
Plasma stage:  12%|█▏        | 0.002468/0.020000 m [00:00]
Plasma stage:  16%|█▌        | 0.003117/0.020000 m [00:00]
Plasma stage:  19%|█▉        | 0.003766/0.020000 m [00:00]
Plasma stage:  22%|██▏       | 0.004416/0.020000 m [00:00]
Plasma stage:  25%|██▌       | 0.005065/0.020000 m [00:00]
Plasma stage:  29%|██▊       | 0.005714/0.020000 m [00:01]
Plasma stage:  32%|███▏      | 0.006364/0.020000 m [00:01]
Plasma stage:  35%|███▌      | 0.007013/0.020000 m [00:01]
Plasma stage:  38%|███▊      | 0.007662/0.020000 m [00:01]
Plasma stage:  42%|████▏     | 0.008312/0.020000 m [00:01]
Plasma stage:  45%|████▍     | 0.008961/0.020000 m [00:01]
Plasma stage:  48%|████▊     | 0.009610/0.020000 m [00:01]
Plasma stage:  51%|█████▏    | 0.010260/0.020000 m [00:01]
Plasma stage:  55%|█████▍    | 0.010909/0.020000 m [00:01]
Plasma stage:  58%|█████▊    | 0.011558/0.020000 m [00:02]
Plasma stage:  61%|██████    | 0.012208/0.020000 m [00:02]
Plasma stage:  64%|██████▍   | 0.012857/0.020000 m [00:02]
Plasma stage:  68%|██████▊   | 0.013506/0.020000 m [00:02]
Plasma stage:  71%|███████   | 0.014156/0.020000 m [00:02]
Plasma stage:  74%|███████▍  | 0.014805/0.020000 m [00:02]
Plasma stage:  77%|███████▋  | 0.015455/0.020000 m [00:02]
Plasma stage:  81%|████████  | 0.016104/0.020000 m [00:02]
Plasma stage:  84%|████████▍ | 0.016753/0.020000 m [00:02]
Plasma stage:  87%|████████▋ | 0.017403/0.020000 m [00:03]
Plasma stage:  90%|█████████ | 0.018052/0.020000 m [00:03]
Plasma stage:  94%|█████████▎| 0.018701/0.020000 m [00:03]
Plasma stage:  97%|█████████▋| 0.019351/0.020000 m [00:03]
Plasma stage: 100%|██████████| 0.020000/0.020000 m [00:03]
Plasma stage: 100%|██████████| 0.020000/0.020000 m [00:03]

Drift
-----
Length = 0.1000 m
CSR off.

Tracking in 10 step(s)... [--                  ]
Tracking in 10 step(s)... [----                ]
Tracking in 10 step(s)... [------              ]
Tracking in 10 step(s)... [--------            ]
Tracking in 10 step(s)... [----------          ]
Tracking in 10 step(s)... [------------        ]
Tracking in 10 step(s)... [--------------      ]
Tracking in 10 step(s)... [----------------    ]
Tracking in 10 step(s)... [------------------  ]
Tracking in 10 step(s)... [--------------------] Done (0.014899253845214844 s).
--------------------------------------------------------------------------------

Active plasma lens:   0%|          | 0.000000/0.020000 m [00:00]
Active plasma lens:  20%|█▉        | 0.004000/0.020000 m [00:00]
Active plasma lens: 100%|██████████| 0.020000/0.020000 m [00:00]

Drift
-----
Length = 0.1000 m
CSR off.

Tracking in 10 step(s)... [--                  ]
Tracking in 10 step(s)... [----                ]
Tracking in 10 step(s)... [------              ]
Tracking in 10 step(s)... [--------            ]
Tracking in 10 step(s)... [----------          ]
Tracking in 10 step(s)... [------------        ]
Tracking in 10 step(s)... [--------------      ]
Tracking in 10 step(s)... [----------------    ]
Tracking in 10 step(s)... [------------------  ]
Tracking in 10 step(s)... [--------------------] Done (0.01707625389099121 s).
--------------------------------------------------------------------------------

Analyze beam evolution

import matplotlib.pyplot as plt
from wake_t.diagnostics import analyze_bunch_list

params_evolution = analyze_bunch_list(bunch_list)

# Quick plot of results.
z = params_evolution["prop_dist"] * 1e2
fig_1 = plt.figure()
plt.subplot(411)
plt.semilogy(z, params_evolution["beta_x"])
plt.tick_params(axis="x", which="both", labelbottom=False)
plt.ylabel("$\\beta_x$ [m]")
plt.subplot(412)
plt.semilogy(z, params_evolution["gamma_x"])
plt.tick_params(axis="x", which="both", labelbottom=False)
plt.ylabel("$\\gamma_{x}$ [$m^{-1}$]")
plt.subplot(413)
plt.plot(z, params_evolution["emitt_x"] * 1e6)
plt.tick_params(axis="x", which="both", labelbottom=False)
plt.ylabel("$\\epsilon_{nx}$ [$\\mu$m]")
plt.subplot(414)
plt.plot(z, params_evolution["avg_ene"] * 0.511)
plt.xlabel("z [cm]")
plt.ylabel("E [MeV]")
plt.tight_layout()

/home/docs/checkouts/readthedocs.org/user_builds/wake-t/envs/stable/lib/python3.11/site-packages/aptools/data_analysis/beam_diagnostics.py:524: RuntimeWarning: invalid value encountered in sqrt
  em_x = np.sqrt(np.linalg.det(cov_x.astype(np.float32, copy=False)))