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A SIMULATION OF THE PHOTOIONIZATION OF H- TOGETHER WITH
THE SUBSEQUENT TRACKING OF THE LIBERATED ELECTRONS*
R. Thurman-Keup†, M. El Baz, V. Scarpine
Fermi National Accelerator Laboratory, Batavia, USA
Abstract
The Proton Improvement Plan - II (PIP-II) is a new linear accelerator (LINAC) complex being built at Fermilab.
It is based on superconducting radiofrequency cavities andwill accelerate H- ions to 800 MeV kinetic energy before
injection into the existing Booster ring. Measurements ofthe profile of the beam along the LINAC must be done by
non-intercepting methods due to the superconducting cavities. The method chosen is photoionization of a small
number of H- by a focused infrared laser, aka laserwire.
The number of ionized electrons is measured as a functionof laser position within the H- beam. To aid in the designof the collection mechanism, a simulation was written in
MATLAB with input from the commercial electromagnetic
simulation, CST. This simulation calculates the number
and positions of the liberated electrons and tracks themthrough the magnetic collection and H- beam fields to thecollection point. Results from this simulation for various
points along the LINAC will be shown.

INTRODUCTION
Fermilab is in the process of constructing a new superconducting (SC) linear accelerator to replace the existingnormal conducting LINAC. This project is called the Proton Improvement Plan - II (PIP-II) [1] and is being built toincrease the deliverable beam intensity to the Deep Underground Neutrino Experiment being constructed in South
Dakota. Since the LINAC is mostly superconducting, theuse of physical wire scanners as beam profilers is not allowed in much of the LINAC due to the risk of a broken
wire contaminating the SC cavities. As the beam is composed of H- ions, laserwires [2, 3] were chosen as the profiler. A laserwire functions by photoionization of the extra
electron on the H- ion using a focused laser. The binding
energy of the extra electron is only 0.7542 eV and can be
ionized by a 1064 nm YAG laser. The ionized electrons,
which are proportional in number to the local density of
H- ions, are collected as the laser is moved through the
H- beam, enabling reconstruction of the profile of thebeam. Due to the complexity of the system, a simulation
was developed to aid in the planning of the laser optics andthe electron collection and is presented in this paper.

EXPERIMENTAL DEVICE
The laserwire system for PIP-II is comprised of a source
laser that is transported through a pipe from the laser room
to the H- beamline (Fig. 1). The pipe is under vacuum to___________________________________________* This manuscript has been authored by Fermi Research Alliance, LLC
under Contract No. DE-AC02-07CH11359 with the U.S. Department ofEnergy, Office of Science, Office of High Energy Physics.
† keup@fnal.gov

both reduce distortions from air currents and to serve as asafety interlock system. At each measurement location(station), there is an insertable mirror to direct the laser
down to the beamline.

Laser
Vacuum Pipefor
Laser Transport

Pickoff
MirrorBox

Laser
Scanning
Boxes

H- BeamFigure 1: Diagram of laser transport. The laser originatesin the laser room and is transported through a vacuum line
to the end of the LINAC. At each laserwire, a vertical pipe
can direct the laser to the H- beamline.
The optical system at the beamline is comprised of movable stages to scan the laser across the H- beam and to select vertical or horizontal scan mode (Fig. 2).
StagesMagnets

Laser

Laser
Scanning
Optics

H- BeamStage

Figure 2: Optics inside the laser scanning box. There arelinear stages to pick horizontal or vertical scan, and to do
the scans.
There are 12 beamline stations with the locations andbeam parameters summarized in Table 1 (plus an additional emittance measuring one after the LINAC). The laserwires are installed just downstream of the location column entry which specifies the cryomodule section and thecryomodule number within that section. The optics within
the beamline stations focus the laser from a large incoming
rms size of ~5 mm to a focused rms size of <100 μm. The
focusing distance will be approximately 300 mm. Once thelaser has ionized the H- beam, the electrons are bent vertically upward to a detector which will nominally be a faraday cup (Fig. 3).

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SIMULATIONThe simulation is comprised of three parts: the calculation of the number of photoionizations and generation of
the electrons, the calculation of the electromagnetic fieldsof the beam and the magnet, and the tracking of the electrons to the detector.
Table 1: Laserwire Locations and Expected Beam Parameters
Laserwire
Location

Position
[m]

MEBT
HWR
SSR1 CM #1
SSR2 CM #2
SSR2 CM #4
SSR2 CM #6
LB650 CM #1
LB650 CM #3
LB650 CM #6
LB650 CM #9
HB650 CM #2
HB650 CM #4

18.7
25.4
31.6
51.5
65.2
78.9
93.4
107.1
127.6
148.0
170.5
192.9

Beam Parameters
Ek
σx
σy
σt
[MeV] [mm] [mm] [ps]2.1
2.3
2.3 208
10.0
1.3
1.4
33
18.6
1.2
1.2
20
61.2
1.4
1.5
13
106.0
1.3
1.3
13
153.9
1.4
1.4
11
192.2
2.3
2.4 6.7
267.4
1.8
1.9 5.7
400.9
1.9
2.0 5.2516.5
2.1
1.8 5.0652.6
1.8
1.9 4.4
833.3
1.5
1.9 3.7
Laser

Magnets

Faraday
Cupwhere 𝜆 is the laser wavelength in the lab frame.
For the PIP-II laserwire design, the laser is transverse to
the H- beam and as such, the square root term in Eq. (1)and the denominator in Eq. (2) are both equal to 1. The Lorentz-transformed laser wavelength shifts from 1064 nm in
the lab frame to 1062 nm in the MEBT and to 883 nm at
the end of the LINAC. The cross sections, 𝜎 , are extracted
at the desired wavelengths from a polynomial fit to Table
IV in reference [5].
The simulation code is written in MATLAB [6]. It steps
through time and calculates the number of ionized electrons on a predefined set of physical mesh points. The simulation utilizes one of two possible numerical mesh arrangements, laser grid or beam grid, depending on the laserand H- beam parameters.
The laser grid approach creates a fixed cylindrical meshaxially aligned with the laser and covering the overlap region of the laser and the H- beam (Fig. 4). The mesh is anelliptic cylinder with radii that scale with the transverse laser size. This keeps the mesh size proportional to the laser
width and avoids losing resolution near the laser waist.
This works well when the laser intensity is low enough to
avoid significant depletion of the H- beam which is not accounted for in this approach.

Laser waist
detailspreserved

Electrons

Figure 4: Laser grid version of the mesh points. The meshspacing scales with the diameter of the laser as it propagates though the H- beam.
Figure 3: The incoming H- beam is partially ionized by thelaser and the electrons are bent vertically by a magnet to a
faraday cup. The blue volume is the vacuum chamber.

Photoionization Simulation
Calculation of the number of photoionizations requires
the particle densities of both the incoming laser and
H- beams, and the cross section for photoionization
𝑑𝑛 = 𝑐𝜎𝑙 − 𝛽⃗− 𝑙 × 𝛽⃗𝐼 𝐼 𝑑𝑡𝑑𝑥𝑑𝑦𝑑𝑧

𝜆 = 𝜆

1 − 𝑙 ⋅ 𝛽⃗

H- BeamDepleted(1)

Here 𝑐 is the speed of light, 𝑙 is the laser beam direction, 𝛽⃗
is the H- beam velocity vector divided by 𝑐, the square root
is a Lorentz-transformed relative velocity term [4], 𝐼 and
𝐼 are the laser and H- number densities respectively, and𝜎 is the photoionization cross section in the frame of the
H- as a function of the laser wavelength Lorentz-transformed to the frame of the H1−𝛽The beam grid version is a rectangular fixed mesh covering the physical overlap region of the laser and theH- beam. The simulated time steps have a spacing that isequal to the physical mesh spacing divided by the H- beam
velocity. This relationship means that with every time step,
the H- beam moves one spatial step, allowing for the fixed
mesh to handle depletion of the H- (Fig. 5).

(2)

Laser

Figure 5: Beam grid version of the mesh points showing
the H- beam intensity. Note the depletion of the H- beam
as it passes through the laser.
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Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
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In both cases, the mesh extent is determined from thespace-time interaction region of the laser and H- while thedesired number of mesh points is set by the user to avoid
loss of details such as the laser waist.
Electrons for tracking are generated from the space-timemesh containing the calculated number of photoionizations. A Poisson distribution is utilized for up to 500 electrons, beyond which a Gaussian approximation is used.
The electrons are given momenta based on the 6D phasespace specified for the H- beam (Fig. 6).

electrons from leaving. As with the bunch fields, theseelectrostatic results are also stored for later use.
ElectronCollection
PoleElectromagnetic Field Calculations
The electromagnetic field calculations involve two separate parts: the fields of the H- beam, and the static fields
of both the electron collection magnets and possibly secondary electron containment electrodes.
The beam field calculation is done in MATLAB and uses
a single bunch which can have any arbitrary shape and size,
but a single fixed velocity. For PIP-II, the H- beam isbunched at a frequency of 162.5 MHz and we use a gaussian shape in all three dimensions. The fields are evaluatedon a rectangular mesh containing an inner section with generally closer spacing to resolve the fields within the bunch,
and an outer section with larger spacing. The fields at eachmesh point are a numerical integration over the bunchcharge. This numerical integration requires a mesh of thebunch as well. To reduce numerical errors, the field evaluation mesh spacing is adjusted such that it is an integer
multiple of the bunch mesh spacing. The results of the field
evaluation are stored for later use by the tracking simulation.

Figure 7: CST calculation of magnetic field of magnets forelectron collection. The plot shows transverse magnetic
field integrated along H- beam direction for 5 different
transverse locations.

Tracking Simulation
The tracking simulation is written in MATLAB and wascreated originally to track electrons in the electron beamprofiler [8] and ionization profile monitors [9]. It tracks theelectrons through static fields and the fields of theH- bunches but does not do self-interactions with the otherelectrons since the effect is generally much smaller than the
H- bunches. It uses an adaptive Runge-Kutta method [10]to solve the pseudo-relativistic second-order differential
equation of motion
𝑑𝑝⃗
𝑑 𝛾𝑣⃗
=𝑚
𝑑𝑡
𝑑𝑡
𝐹⃗ 𝑟⃗, 𝑡 = 𝑚𝛾 𝑎⃗ + 𝛾 𝛽⃗ 𝛽⃗ ⋅ 𝑎⃗𝐹⃗ 𝑟⃗, 𝑡 =(3)which, when inverted to find 𝑎⃗, is
𝑎⃗ =

𝑑 𝑟⃗
1
=
𝑰 − 𝛽⃗𝛽⃗ 𝐹⃗ 𝑟⃗, 𝑡
𝛾𝑚
𝑑𝑡

(4)

where 𝐹⃗ 𝑟⃗, 𝑡 = 𝑞 𝐸⃗ 𝑟⃗, 𝑡 + 𝑣⃗ × 𝐵⃗ 𝑟⃗, 𝑡 , 𝑚 is the massof the particle being tracked, 𝛾 = 1⁄ 1 − 𝛽 is the Lorentz factor, and 𝑰 is the identity matrix. We apply the
Runge-Kutta method to the second-order differential equation rewritten as coupled first order differential equations

Figure 6: Generated electron distributions. The laser waist
can be seen in the x position distribution. A 3D distributionof the electron positions is shown in the red box where thelaser waist can be seen again.
The static fields are calculated in CST [7] which is a 3D
electromagnetic simulation. We designed a magnet with areturn yoke to reduce the impact on the H- beam (Fig. 7).
In addition, we will also add a small quadrupole magnet for
the MEBT laserwire to compensate electron spreadingfrom H- space charge forces. When the electrons strike thefaraday cup, they generate secondary electrons that may
escape the surface of the faraday cup, altering the collectedcharge. To avoid this, we may need to install a conductive
ring to apply an electrostatic field to keep the secondary1𝑑𝑣⃗=
𝑰 − 𝛽⃗𝛽⃗ 𝐹⃗ 𝑟⃗, 𝑡
𝑑𝑡 𝛾𝑚
(5)
𝑑𝑟⃗
= 𝑣⃗
𝑑𝑡
For each Runge-Kutta time step, the previously stored
bunch and static fields are interpolated to find the value atthe space-time location of the particle being tracked. For
the bunch fields, the field is interpolated to the requested
position after adjusting it for the requested time and the velocity of the bunch,𝐸⃗ 𝐵⃗ 𝑟⃗, 𝑡 → 𝐸⃗ 𝐵⃗ 𝑟⃗ + 𝑣⃗𝑡(6)where 𝑡 = 𝑡 modulo 𝑡 . The modulo function implements a repetitive bunch structure at the specified bunch
spacing, 𝑡 .

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The adaptive part of the algorithm adjusts the step size
to keep changes in the momenta, either absolute value or
direction, within a range specified by thresholds. If any of
the thresholds are exceeded, the step size is adjusted tocompensate.

RESULTS
The simulation has been used to design the collection
magnet and find optimal laser parameters to avoid wasted
laser energy and resolution degradation. Figures 8 and 9
show electron trajectories at two locations: MEBT and
HWR. The MEBT location (Fig. 8) shows tracking resultswith and without a quadrupole field. The extra quadrupole
may be necessary in the MEBT to deal with spreading of
the electrons due to the space charge of the H- beam.
No Quad

a)

Quad

b)

The containment of the electrons is better at this location
since the electrons have higher energy and are less susceptible to H- space charge forces. The initial deflection downin all of these is driven by the positioning of the two magnet yokes where the first corrector yoke is closer to the laser interaction region. This effect helps to increase theclearance between the electrons and the corner of thebeampipes.
Studies were also done to evaluate the photoionization
rates for different length laser pulses, laser arrival time jitter, and H- temporal bunch lengths (Fig. 10). These results
will help to determine the optimal laser properties to maximize signal and resolution while minimizing unused laser
energy which has detrimental effects on the vacuum windows. For instance, from the plots, we can see that laser
pulses with a length of 20 or 30 ps have good photoionization but small variation with jitter.

c)d)Figure 8: MEBT laserwire; a) and b) are the trajectories
looking down from above the beam. They show the difference in final spread between having a quadrupole field andnot having a quadrupole field. Plots c) and d) are the trajectories looking from the side of the beam. They first deviate down before bending up which allows more clearance
between the electrons and the beampipe.
Figure 9 shows trajectories in the laserwire after the
HWR which is the first cryomodule.
b)a)

Number of photoionized electrons (arb. Units)

0.15

Laser Jitter = 0 ps

H- Beam
Length 5 ps
Energy 400 MeV

0.10
0.05
0
100
0.15

Laser Jitter = 5 ps
101

0.10
0.05
0
100
0.10
0.08
0.06
0.04
0.02
0
100

102
Laser Jitter = 0 ps

Laser Jitter = 5 ps
101

103
H- Beam
Length 10 ps
Energy 200 MeV

102
Laser Jitter = 0 ps

Laser Jitter = 5 ps

101 Laser Pulse Length (ps)103
H- Beam
Length 20 ps
Energy 100 MeV

102

103

Figure 10: Study of the effect of laser jitter on the numberof photoionized electrons using the simulation at 3 different H- beam energies.
This simulation was also recently used in an analysis of
a novel bunch length measurement at the Spallation Neutron Source at Oak Ridge National Lab [11].

CONCLUSIONSThis laserwire simulation has proven to be useful for anumber of analyses pertaining to laserwires. From magnet
designs and laser parameter choices to measurement analyses. We foresee even more uses as we proceed to buildand commission the PIP-II laserwire systems.

REFERENCES

c)[1] V. Lebedev et al., “The PIP-II conceptual design report”,
FNAL, Batavia, IL, USA, Rep. FERMILAB-DESIGN2017-01, Mar 2017. doi:10.2172/1346823[2] Y. Liu et al., “Laser based diagnostics for measuring
H- beam parameters”, in Proc. 24th Particle Accelerator
Conf. (PAC’11), New York, NY, USA, Mar.-Apr. 2011, paper WEOCN1, pp. 1433-1437.
https://jacow.org/PAC2011/papers/weocn1.pdf[3] V. Scarpine et al., “Beam profile measurements utilizing anamplitude modulated pulsed fiber laser at PIP2IT”, in Proc.
10th Int. Beam Instrumentation Conf. (IBIC’21), Korea,
Sept 2021, paper TUPP25.

Figure 9: HWR laserwire. Plot a) is the trajectories looking
down from above the beam. b) and c) are the trajectories
looking from the side of the beam.

doi:10.18429/JACoW-IBIC2021-TUPP25[4] L.D. Landau and E.M. Lifshitz, The Classical Theory of
Fields. Oxford, England: Pergamon Press, pp. 34-36, 1975.

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IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 2 4

Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

IBIC2023, Saskatoon, Canada
JACoW Publishing
ISSN: 2 6 7 3 - 5 3 5 0
d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - W E P 0 2 4[5] J.T. Broad and W.P. Reinhardt, “One- and two-electron
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doi:10.1103/PhysRevA.14.2159[6] MathWorks, https://www.mathworks.com[7] Dassault Systemes – Simulia, https://www.3ds.com[8] R. Thurman-Keup et al., “Commissioning and First Resultsof the Electron Beam Profiler in the Main Injector at Fermilab”, in Proc. 6th Int. Beam Instrumentation Conf.
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[9] J.R. Zagel et al., “Third Generation Residual Gas Ionization
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doi:10.18429/JACoW-IBIC2017-WE3AB3

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