A Simulation of the Photoionization of H- Together Withthe Subsequent Tracking of the Liberated Electrons*

FERMILAB-POSTER-23-294-AD

R. Thurman-Keup#, M. El Baz, V. Scarpine,Fermi National Accelerator Laboratory, Batavia, USAWEP024
Abstract
The Proton Improvement Plan - II (PIP-II) is a new linear accelerator(LINAC) complex being built at Fermilab. It is based onsuperconducting radiofrequency cavities and will accelerate H- ionsto 800 MeV kinetic energy before injection into the existing Boosterring. Measurements of the profile of the beam along the LINAC mustbe 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 ionizedelectrons is measured as a function of laser position within the Hbeam. To aid in the design of the collection mechanism, a simulation
was written in MATLAB with input from the commercial
electromagnetic simulation, CST. This simulation calculates thenumber and positions of the liberated electrons and tracks themthrough the magnetic collection and H- beam fields to the collectionpoint. Results from this simulation for various points along the LINAC
will be shown.

Experimental Device

Photoionization Simulation
The simulation code is written in MATLAB [6]. It steps throughtime and calculates the number of ionized electrons on apredefined set of physical mesh points. The simulation utilizes
one of two possible numerical mesh arrangements, laser grid orbeam grid, depending on the laser and H- beam parameters.

Laser

Laser Scanning Box optics showing moving stages for scanning.
The laser originates in the laser room and is transported througha vacuum line to the end of the LINAC. At each laserwire, avertical pipe can direct the laser to the H- beamline.

StagesPickoffMirror
BoxVacuum PipeforLaser Transport

Electrons

Magnets

H- Beam

Laser
Scanning
Boxes

H- Beam

Laserwire positions and associated beam parameters

Stage

Electromagnetic Field Calculations

Photoionization Theory

The electromagnetic field calculations involve two separate parts: the fields of the H- beam, andthe static fields of both the electron collection magnets and possibly secondary electron
containment electrodes.

The number of photoionizations depends on the particle
densities of both the incoming laser, 𝐼𝑙 , and H- beam, 𝐼𝑏 , and thecross section for photoionization, 𝜎𝐼 ,𝑑𝑛 = 𝑐𝜎𝐼𝑙መ − 𝛽Ԧ2− 𝑙መ × 𝛽Ԧ

2Faraday
CupLaser
Magnets

Laser

Introduction
Fermilab is in the process of constructing a new super-conducting(SC) linear accelerator to replace the existing normal conducting
LINAC. This project is called the Proton Improvement Plan - II (PIP-II)[1] and is being built to increase the deliverable beam intensity tothe Deep Underground Neutrino Experiment being con-structed inSouth Dakota. Since the LINAC is mostly superconducting, the use ofphysical wire scanners as beam profilers is not allowed in much of
the LINAC due to the risk of a broken wire contaminating the SCcavities. As the beam is composed of H- ions, laserwires [2,3] werechosen 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 bya 1064 nm YAG laser. The ionized electrons, which are proportionalin number to the local density of H- ions, are collected as the laser ismoved through the H- beam, enabling reconstruction of the profileof the beam.

The incoming H- beam is partially ionized by the laser andthe electrons are bent vertically by a magnet to a faradaycup. The blue volume is the vacuum chamber.

𝐼𝑙 𝐼𝑏 𝑑𝑡𝑑𝑥𝑑𝑦𝑑𝑧

Bunch Fields
The beam field calculation is done in MATLAB and uses a single bunch which can haveany arbitrary shape and size, but a single fixed velocity. The fields are evaluated on arectangular mesh containing an inner section with generally closer spacing to resolve thefields within the bunch, and an outer section with larger spacing. The fields at eachmesh point are a numerical integration over the bunch charge. This numericalintegration requires a mesh of the bunch as well. To reduce numerical errors, the field
evaluation mesh spacing is adjusted such that it is an integer multiple of the bunch meshspacing.
Line of mesh values

with 𝑙መ and 𝛽Ԧ being the laser and H- normalized velocity vectors.
See [4] for the origin of the square root multiplier. The crosssection depends on the laser wavelength in the frame of the H-,
𝜆ሚ 𝑙 ,
1 − 𝛽2
𝜆ሚ 𝑙 = 𝜆𝑙
1 − 𝑙መ ⋅ 𝛽ԦFor orthogonal beams, the two equations reduce to𝑑𝑛 = 𝑐𝜎𝐼 𝐼𝑙 𝐼𝑏 𝑑𝑡𝑑𝑥𝑑𝑦𝑑𝑧
𝜆ሚ 𝑙 = 𝜆𝑙 1 − 𝛽 2Laserwire
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 ParametersEkσxσyσt[MeV] [mm] [mm] [ps]2.1
2.3
2.3 208
10.0
1.3
1.4 3318.6
1.2
1.2 2061.2
1.4
1.5 13106.0 1.3
1.3 13153.9 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 5.2
516.5 2.1
1.8 5.0652.6 1.8
1.9 4.4
833.3 1.5
1.9 3.7

Static Fields
The static fields are calculated in CST [7] which is a 3D electromagnetic simulation. We
designed a magnet with a return yoke to reduce the impact on the H- beam. In addition,
we will also add a small quadrupole magnet for the MEBT laserwire to compensate
electron spreading from H- space charge forces. When the electrons strike the faradaycup, they generate secondary electrons that
may escape the surface of the faraday cup,
altering the collect-ed charge. To avoid this,we may need to install a conductive ring toapply an electrostatic field to keep thesecondary electrons from leaving.

Electron Collection Pole
Course mesh

Fine mesh

Laser Grid
Uses a fixed cylindrical mesh axiallyaligned with the laser and covering
the overlap region of the laser andthe H- beam. The mesh is anelliptic cylinder with radii that scalewith the transverse laser size. This
keeps the mesh size proportional
to the laser width and avoids losing
resolution near the laser waist.
Used when the laser intensity is
low enough that depletion of theH- is not important.

Laser waist
detailspreserved

H- BeamDepleted

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
the electrons through static fields and the fields of the Hbunches but does not do self-interactions with the otherelectrons. It uses an adaptive Runge-Kutta method [10]to solve the pseudo-relativistic second-order differential
equation of motion
𝑑𝑝Ԧ
𝑑 𝛾 𝑣Ԧ
𝐹Ԧ 𝑟,
Ԧ𝑡 ==𝑚𝑑𝑡
𝑑𝑡𝐹Ԧ 𝑟,Ԧ 𝑡 = 𝑚𝛾 𝑎Ԧ + 𝛾 2 𝛽Ԧ 𝛽Ԧ ⋅ 𝑎Ԧ
which, when inverted to find 𝑎,
Ԧ is𝑑 2 𝑟Ԧ
1𝑎Ԧ = 2 =𝑰 − 𝛽Ԧ 𝛽Ԧ𝑇 𝐹Ԧ 𝑟,Ԧ𝑡𝑑𝑡
𝛾𝑚where 𝐹Ԧ 𝑟,
Ԧ 𝑡 = 𝑞 𝐸 𝑟,
Ԧ 𝑡 + 𝑣Ԧ × 𝐵 𝑟,
Ԧ 𝑡 , 𝑚 is the massof the particle being tracked, 𝛾 = 1Τ 1 − 𝛽 2 is theLorentz factor, and 𝑰 is the identity matrix. We apply theRunge-Kutta method to the second-order differential
equation rewritten as coupled first order differential
equations𝑑𝑣Ԧ
1=𝑰 − 𝛽Ԧ 𝛽Ԧ 𝑇 𝐹Ԧ 𝑟,
Ԧ𝑡
𝑑𝑡 𝛾𝑚𝑑 𝑟Ԧ
= 𝑣Ԧ
𝑑𝑡
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,

Uses a rectangular fixed meshcovering the physical overlap
region of the laser and the Hbeam. The simulated time steps
have a spacing that is equal tothe physical mesh spacing
divided by the H- beam velocity.
This relation-ship means thatwith every time step, the Hbeam moves one spatial step,
allowing for the fixed mesh tohandle depletion of the H- beam.

𝐸 ቚ𝐵 𝑟,Ԧ 𝑡 → 𝐸 ቚ𝐵 𝑟Ԧ + 𝑣𝑡
Ԧ 𝑚
where 𝑡𝑚 = 𝑡 modulo 𝑡𝑏 . The modulo function
implements a repetitive bunch structure at the specified
bunch spacing, 𝑡𝑏 .
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 isadjusted to compensate.

Number of photoionized electrons (arb. Units)

0.15

Laser Jitter = 0 ps

0100
0.15

Laser Jitter = 5 ps
101

0.05
0100
0.10
0.08
0.06
0.04
0.02
0100

102

Laser Jitter = 0 ps

0.10d)MEBT laserwirec) and d) are the trajectories looking from the side of the beam. They firstdeviate down before bending up which allows more clearance between theelectrons and the beampipe.

b)

103

102
Laser Jitter = 0 psc)

103
H- Beam
Length 20 ps
Energy 100 MeV

Laser Jitter = 5 ps

101 Laser Pulse Length (ps)

Quadb)c)a)

H- Beam
Length 10 ps
Energy 200 MeV

Laser Jitter = 5 ps
101No Quada)

H- Beam
Length 5 ps
Energy 400 MeV

0.10
0.05

MEBT laserwirea) and b) are the trajectories looking down from above the beam. They show
the difference in final spread between having a quadrupole field and nothaving a quadrupole field.

HWR laserwire (after 1st cryomodule)a) is the trajectories looking down from above the beam. Notice that thecontainment is much better even without the quadrupole since the energy ishigh enough to prevent significant spreading from H- space charge.
b) and c) are the trajectories looking from the side of the beam.

Studies were done to evaluate the photoionization rates for different length laser
pulses, laser arrival time jitter, and H- temporal bunch lengths. 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.

Electron Generation
Electrons for tracking are generated from the space-time mesh containing the calculated number ofphotoionizations. 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 phase space specified for the H- beam.

Tracking Simulation

Beam GridLaser

Longitudinal
Integral ofMagnetic
Field

102103

3D distribution ofelectrons. The laser
waist is evident here.

* This manuscript has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359
with the U.S. Department of Energy, Office of Science, Office of High Energy Physics.
# keup@fnal.gov

REFERENCES[1] V. Lebedev et al., “The PIP-II conceptual design report”, FNAL, Batavia, IL, USA, Rep. FERMILAB-DESIGN-2017-01, Mar 2017. doi:10.2172/1346823[2] Y. Liu et al., “Laser based diagnostics for measuring H- beam parameters”, in Proc. PAC’11, New York, NY, USA, Mar.-Apr. 2011, pp. 1433-1437. https://accelconf.web.cern.ch/PAC2011/papers/weocn1.pdf[3] V. Scarpine et al., “Beam profile measurements utilizing an amplitude modulated pulsed fiber laser at PIP2IT”, in Proc. IBIC’21, Korea, Sept 2021. doi:10.18429/JACoW-IBIC2021-TUPP25[4] L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields. Oxford, England: Pergamon Press, 1975, pp. 34-36.
[5] J.T. Broad and W.P. Reinhardt, “One- and two-electron photoejection from H−: A multichannel J-matrix calculation”, Phys. Rev. A, vol. 14, p. 2159, 1976. 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 Results of the Electron Beam Profiler in the Main Injector at Fermilab”, in Proc. IBIC'17, Grand Rapids, MI, USA, Aug. 2017, pp. 330-334. doi:10.18429/JACoW-IBIC2017-WE3AB3[9] J.R. Zagel et al., “Third Generation Residual Gas Ionization Profile Monitors at Fermilab”, in Proc. IBIC’14, Monterey, CA, USA, Sep. 2014, pp. 408-411. https://jacow.org/IBIC2014/papers/tupd04.pdf[10] https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods[11] Y. Liu et al., “Longitudinal bunch profile measurement of operational H- beam using laser wire and virtual slit”, Phys. Rev. Accel. Beams, vol. 26, p. 042801, 2023. doi:10.1103/PhysRevAccelBeams.26.042801