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Book Ion Acceleration from the Interaction of Ultra intense Lasers with Solid Foils

Download or read book Ion Acceleration from the Interaction of Ultra intense Lasers with Solid Foils written by Matthew Mark Allen and published by . This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Ion Acceleration from the Interaction of Ultra Intense Lasers with Solid Foils

Download or read book Ion Acceleration from the Interaction of Ultra Intense Lasers with Solid Foils written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery that ultra-intense laser pulses (I> 10[sup 18] W/cm[sup 2]) can produce short pulse, high energy proton beams has renewed interest in the fundamental mechanisms that govern particle acceleration from laser-solid interactions. Experiments have shown that protons present as hydrocarbon contaminants on laser targets can be accelerated up to energies> 50 MeV. Different theoretical models that explain the observed results have been proposed. One model describes a front-surface acceleration mechanism based on the ponderomotive potential of the laser pulse. At high intensities (I> 10[sup 18] W/cm[sup 2]), the quiver energy of an electron oscillating in the electric field of the laser pulse exceeds the electron rest mass, requiring the consideration of relativistic effects. The relativistically correct ponderomotive potential is given by U[sub p] = ([1 + I[lambda][sup 2]/1.3 x 10[sup 18]][sup 1/2] - 1) m[sub o]c[sup 2], where I[lambda][sup 2] is the irradiance in W [micro]m[sup 2]/cm[sup 2] and m[sub o]c[sup 2] is the electron rest mass. At laser irradiance of I[lambda][sup 2] [approx] 10[sup 20] W [micro]m[sup 2]/cm[sup 2], the ponderomotive potential can be of order several MeV. A few recent experiments--discussed in Chapter 3 of this thesis--consider this ponderomotive potential sufficiently strong to accelerate protons from the front surface of the target to energies up to tens of MeV. Another model, known as Target Normal Sheath Acceleration (TNSA), describes the mechanism as an electrostatic sheath on the back surface of the laser target. According to the TNSA model, relativistic hot electrons created at the laser-solid interaction penetrate the foil where a few escape to infinity. The remaining hot electrons are retained by the target potential and establish an electrostatic sheath on the back surface of the target. In this thesis we present several experiments that study the accelerated ions by affecting the contamination layer from which they originate. Radiative heating was employed as a method of removing contamination from palladium targets doped with deuterium. We present evidence that ions heavier than protons can be accelerated if hydrogenous contaminants that cover the laser target can be removed. We show that deuterons can be accelerated from the deuterated-palladium target, which has been radiatively heated to remove contaminants. Impinging a deuteron beam onto a tritiated-titanium catcher could lead to the development of a table-top source of short-pulse, 14-MeV fusion neutrons. We also show that by using an argon-ion sputter gun, contaminants from one side of the laser target can be selectively removed without affecting the other side. We show that irradiating a thin metallic foil with an ultra-intense laser pulse produces a proton beam with a yield of 1.5-2.5 10[sup 11] and temperature, kT = 1.5 MeV with a maximum proton energy> 9 MeV. Removing contaminants from the front surface of the laser target with an argon-ion sputter gun, had no observable effect on the proton beam. However, removing contaminants from the back surface of the laser target reduced the proton beam by two orders of magnitude to, at most, a yield of [approx] 10[sup 9] and a maximum proton energy 4 MeV. Based on these observations, we conclude that the majority ( 99%) of high energy protons (E> 5 MeV) from the interaction of an ultra-intense laser pulse with a thin foil originate on the back surface of the foil--as predicted by the TNSA model. Our experimental results are in agreement with PIC simulations showing back surface protons reach energies up to 13 MeV, while front surface protons reach a maximum energy of 4 MeV. Well diagnosed and controllable proton beams will have many applications: neutron radiography, material damage studies, production of medical isotopes, and as a high-resolution radiography tool for diagnosing opaque materials and plasmas. Well collimated and focusable ion beams may also prove beneficial for alternative inertial-fusion concepts such as proton fast ignition, a potentially viable method for achieving a controlled fusion reaction in the laboratory earlier than expected.

Book Laser Ion Acceleration from the Interaction of Ultra Intense Laser Pulse with Thi Foils

Download or read book Laser Ion Acceleration from the Interaction of Ultra Intense Laser Pulse with Thi Foils written by and published by . This book was released on 2004 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery that ultra-intense laser pulses (I> 1018 W/cm2) can produce short pulse, high energy proton beams has renewed interest in the fundamental mechanisms that govern particle acceleration from laser-solid interactions. Experiments have shown that protons present as hydrocarbon contaminants on laser targets can be accelerated up to energies> 50 MeV. Different theoretical models that explain the observed results have been proposed. One model describes a front-surface acceleration mechanism based on the ponderomotive potential of the laser pulse. At high intensities (I> 1018 W/cm2), the quiver energy of an electron oscillating in the electric field of the laser pulse exceeds the electron rest mass, requiring the consideration of relativistic effects. The relativistically correct ponderomotive potential is given by Up = ([1 + I[lambda]2/1.3 x 1018]1/2 - 1) moc2, where I[lambda]2 is the irradiance in W[mu]m2/cm2 and moc2 is the electron rest mass. At laser irradiance of I[lambda]2 ~ 1018 W[mu]m2/cm2, the ponderomotive potential can be of order several MeV. A few recent experiments--discussed in Chapter 3 of this thesis--consider this ponderomotive potential sufficiently strong to accelerate protons from the front surface of the target to energies up to tens of MeV. Another model, known as Target Normal Sheath Acceleration (TNSA), describes the mechanism as an electrostatic sheath on the back surface of the laser target. According to the TNSA model, relativistic hot electrons created at the laser-solid interaction penetrate the foil where a few escape to infinity. The remaining hot electrons are retained by the target potential and establish an electrostatic sheath on the back surface of the target.

Book Ion acceleration and extreme light field generation based on ultra short and ultra   intense lasers

Download or read book Ion acceleration and extreme light field generation based on ultra short and ultra intense lasers written by Liangliang Ji and published by Springer Science & Business Media. This book was released on 2014-01-23 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the relativistic (laser intensity above 1018 W/cm2) laser-plasma interactions, which mainly concerns two important aspects: ion acceleration and extreme-light-field (ELF). Based on the ultra-intense and ultra–short CP lasers, this book proposes a new method that significantly improves the efficiency of heavy-ion acceleration, and deals with the critical thickness issues of light pressure acceleration. More importantly, a series of plasma approaches for producing ELFs, such as the relativistic single-cycle laser pulse, the intense broad-spectrum chirped laser pulse and the ultra-intense isolated attosecond (10-18s) pulse are introduced. This book illustrates that plasma not only affords a tremendous accelerating gradient for ion acceleration but also serves as a novel medium for ELF generation, and hence has the potential of plasma-based optics, which have a great advantage on the light intensity due to the absence of device damage threshold.

Book Ion Acceleration in Ultra thin Foils Undergoing Relativistically Induced Transparency

Download or read book Ion Acceleration in Ultra thin Foils Undergoing Relativistically Induced Transparency written by Haydn W. Powell and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis reports on experimental and numerical investigations of ion acceleration and the underlying mechanisms of energy transfer in the interaction of intense laser pulses with ultra-thin foils undergoing relativistic induced transparency. The optimisation and optical control of the ion beam properties including the beam flux, maximum energy and energy spread is important for the development of applications of laser-driven ion beams. Multiple laser-ion acceleration mechanisms, driven by sheath fields, radiation pressure and transparency enhancement occur in intense laser pulse interactions with an ultra-thin foil. This is experimentally and numerically demonstrated in the work presented in this thesis. Results from an experimental investigation of ion acceleration from ultra-thin (nanometer-thick) foils using the Vulcan petawatt laser facility are presented. Spatially separating the multiple beam components arising from the differing acceleration mechanisms enables the underlying physics of the individual mechanisms to be investigated. In the case of foils undergoing relativistic induced transparency, it is shown that an extended channel and resulting jet is formed in the expanding plasma at the rear of the target, resulting in higher laser energy absorption into electrons and enhanced ion acceleration in a localised region. This results from volumetric heating of electrons by the laser pulse propagating within the channel. The measured maximum energy of the protons in the enhanced region of the jet is found to be highly sensitive to the laser pulse contrast and rising edge intensity profile of the laser. It is shown, using a controlled pre-expansion of the target, that an increase in the maximum proton energy by a factor two is achievable. Numerical investigations of the interaction, using particle-in-cell (PIC) simulations, show that an idealised sharp rising edge Gaussian laser intensity profile produces the highest proton energy, though this condition could not be achieved experimentally. The simulations show that controlled pre-expansion of the target, by variation of the rising edge intensity profile, enables better conditions for channel formation and energy coupling to electrons and thus protons. A detailed numerical (PIC) investigation of the mechanisms of laser energy transfer to electrons and ions in thin foils undergoing relativistically induced transparency is also presented. The role of streaming instabilities in the transfer of energy between particle species is investigated. It is found that in addition to the relativistic Buneman instability, which arises from streaming of the volumetrically heated relativistic electrons with the background ions during transparency, ionion streaming in the expanding plasma also plays a role in enhancing the final ion energy. Enhancement of proton maximum energies via ion-ion streaming from shock-accelerated aluminium ions is observed in 1D PIC simulations and the energy exchange is demonstrated to be sensitive to the plasma density. Energy transfer between co-directional ion species is also observed in higher dimension 2D simulations. The simulations show that the greatest enhancement in proton energy is due to streaming of electrons in the region of the plasma jet formed in the expanding plasma.

Book Relativistically Intense Laser   Microplasma Interactions

Download or read book Relativistically Intense Laser Microplasma Interactions written by Tobias Ostermayr and published by Springer. This book was released on 2019-07-16 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation covers several important aspects of relativistically intense laser–microplasma interactions and some potential applications. A Paul-trap based target system was developed to provide fully isolated, well defined and well positioned micro-sphere-targets for experiments with focused peta-watt laser pulses. The laser interaction turned such targets into microplasmas, emitting proton beams with kinetic energies exceeding 10 MeV. The proton beam kinetic energy spectrum and spatial distribution were tuned by variation of the acceleration mechanism, reaching from broadly distributed spectra in relatively cold plasma expansions to spectra with relative energy spread as small as 20% in spherical multi-species Coulomb explosions and in directed acceleration processes. Numerical simulations and analytical calculations support these experimental findings and show how microplasmas may be used to engineer laser-driven proton sources. In a second effort, tungsten micro-needle-targets were used at a peta-watt laser to produce few-keV x-rays and 10-MeV-level proton beams simultaneously, both measured to have only few-μm effective source-size. This source was used to demonstrate single-shot simultaneous radiographic imaging with x-rays and protons of biological and technological samples. Finally, the dissertation discusses future perspectives and directions for laser–microplasma interactions including non-spherical target shapes, as well as thoughts on experimental techniques and advanced quantitative image evaluation for the laser driven radiography.

Book Multispecies Ion Acceleration from Intense Laser Interactions with Thin Foils

Download or read book Multispecies Ion Acceleration from Intense Laser Interactions with Thin Foils written by Aodhan McIlvenny and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Investigations of Field Dynamics in Laser Plasmas with Proton Imaging

Download or read book Investigations of Field Dynamics in Laser Plasmas with Proton Imaging written by Thomas Sokollik and published by Springer Science & Business Media. This book was released on 2011-01-12 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laser-driven proton beams are still in their infancy but already have some outstanding attributes compared to those produced in conventional accelerators. One such attribute is the typically low beam emittance. This allows excellent resolution in imaging applications like proton radiography. This thesis describes a novel imaging technique - the proton streak camera - that the author developed and first used to measure both the spatial and temporal evolution of ultra-strong electrical fields in laser-driven plasmas. Such investigations are of paramount importance for the understanding of laser-plasma interactions and, thus, for optimization of laser-driven particle acceleration. In particular, the present work investigated micrometer-sized spherical targets after laser irradiation. The confined geometry of plasmas and fields was found to influence the kinetic energy and spatial distribution of accelerated ions. This could be shown both in experimental radiography images and and in numerical simulations, one of which was selected for the cover page of Physical Review Letters.

Book Intra pulse Dynamics of Laser driven Ion Acceleration in Ultra thin Foils

Download or read book Intra pulse Dynamics of Laser driven Ion Acceleration in Ultra thin Foils written by Hersimerjit Padda and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through variation of the target foil thickness, the opening angle of the ring is shown to be correlated to the point in time during the laser pulse interaction at which the target becomes transparent to the laser (in a process termed relativistic induced transparency). The ring is largest when transparency occurs close to the peak of the laser intensity.

Book Optimisation and Control of Ion Acceleration in Intense Laser foil Interactions

Download or read book Optimisation and Control of Ion Acceleration in Intense Laser foil Interactions written by Adam Higginson and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book New Computational and Experimental Approaches for Studying Ion Acceleration and the Intense Laser plasma Interaction

Download or read book New Computational and Experimental Approaches for Studying Ion Acceleration and the Intense Laser plasma Interaction written by Ginevra E. Cochran and published by . This book was released on 2018 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Advanced Diagnostics for Magnetic and Inertial Fusion

Download or read book Advanced Diagnostics for Magnetic and Inertial Fusion written by Peter E. Stott and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Conference on Advanced Diagnostics for Magnetic and Inertial Fusion, held September 3-7, 2001 at Villa Monastero, Varenna, Italy. This volume focuses on future diagnostic requirements for fusion energy research emphasizing advanced diagnostics, new techniques and areas where further progress is required.

Book Coherence and Ultrashort Pulse Laser Emission

Download or read book Coherence and Ultrashort Pulse Laser Emission written by F. J. Duarte and published by BoD – Books on Demand. This book was released on 2010-12-30 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, recent contributions on coherence provide a useful perspective on the diversity of various coherent sources of emission and coherent related phenomena of current interest. These papers provide a preamble for a larger collection of contributions on ultrashort pulse laser generation and ultrashort pulse laser phenomena. Papers on ultrashort pulse phenomena include works on few cycle pulses, high-power generation, propagation in various media, to various applications of current interest. Undoubtedly, Coherence and Ultrashort Pulse Emission offers a rich and practical perspective on this rapidly evolving field.

Book Advances in Solid State Lasers

Download or read book Advances in Solid State Lasers written by Mikhail Grishin and published by BoD – Books on Demand. This book was released on 2010-02-01 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invention of the solid-state laser has initiated the beginning of the laser era. Performance of solid-state lasers improved amazingly during five decades. Nowadays, solid-state lasers remain one of the most rapidly developing branches of laser science and become an increasingly important tool for modern technology. This book represents a selection of chapters exhibiting various investigation directions in the field of solid-state lasers and the cutting edge of related applications. The materials are contributed by leading researchers and each chapter represents a comprehensive study reflecting advances in modern laser physics. Considered topics are intended to meet the needs of both specialists in laser system design and those who use laser techniques in fundamental science and applied research. This book is the result of efforts of experts from different countries. I would like to acknowledge the authors for their contribution to the book. I also wish to acknowledge Vedran Kordic for indispensable technical assistance in the book preparation and publishing.

Book Ion Acceleration by Laser Plasma Interaction from Cryogenic Microjets

Download or read book Ion Acceleration by Laser Plasma Interaction from Cryogenic Microjets written by and published by . This book was released on 2015 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processes that occur in extreme conditions, such as in the center of stars and large planets, can be simulated in the laboratory using facilities such as SLAC National Accelerator Laboratory and the Jupiter Laser Facility (JLF) at Lawrence Livermore National Laboratory (LLNL). These facilities allow scientists to investigate the properties of matter by observing their interactions with high power lasers. Ion acceleration from laser plasma interaction is gaining greater attention today due to its widespread potential applications, including proton beam cancer therapy and fast ignition for energy production. Typically, ion acceleration is achieved by focusing a high power laser on thin foil targets through a mechanism called Target Normal Sheath Acceleration. However, this mechanism is not ideal for creating the high-energy proton beams needed for future applications. Based on research and recent experiments, we hypothesized that a pure liquid cryogenic jet would be an ideal target for exploring new regimes of ion acceleration. Furthermore, it would provide a continuous, pure target, unlike metal foils which are consumed in the interaction and easily contaminated. In an e ort to test this hypothesis, we used the 527 nm split beam, frequency-doubled TITAN laser at JLF. Data from the cryogenic jets was limited due to the ow of current up the jet into the nozzle during the interaction, heating the jet and damaging the ori ce. However, we achieved a pure proton beam with evidence of a monoenergetic feature. Furthermore, data from gold and carbon wires showed surprising and interesting results. Preliminary analysis of data from two ion emission diagnostics, Thomson parabola spectrometers (TPs) and radio chromic lms (RCFs), suggests that shockwave acceleration occurred rather than target normal sheath acceleration, the standard mechanism of ion acceleration. Upon completion of the experiment at TITAN, I researched the possibility of transforming our liquid cryogenic jets into droplet streams. This type of target should solve our problems with the jet as it will prevent the ow of exocurrent into the nozzle. It is also highly e ective as it is even more mass-limited than standard cryogenic jets. Furthermore, jets break up spontaneously anyway. If we can control the breakup, we can synchronize the droplet emission with the laser pulses. In order to assist the team prepare for an experiment later this year, I familiarized myself with the physics and theory of droplet formation, calculated values for the required parameters, and ordered the required materials for modi cation of the jet. Future experiments will test these droplet streams and continue towards the goal of ion acceleration using cryogenic targets.

Book On the Acceleration and Transport of Electrons Generated by Intense Laser Plasma Interactions at Sharp Interfaces

Download or read book On the Acceleration and Transport of Electrons Generated by Intense Laser Plasma Interactions at Sharp Interfaces written by Joshua Joseph May and published by . This book was released on 2017 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continued development of the chirped pulse amplification technique has allowed for the development of lasers with powers of in excess of $10^{15}W$, for pulse lengths with durations of between .01 and 10 picoseconds, and which can be focused to energy densities greater than 100 giga-atmospheres. When such lasers are focused onto material targets, the possibility of creating particle beams with energy fluxes of comparable parameters arises. Such interactions have a number of theorized applications. For instance, in the Fast Ignition concept for Inertial Confinement Fusion \cite{Tabak:1994vx}, a high-intensity laser efficiently transfers its energy into an electron beam with an appropriate spectra which is then transported into a compressed target and initiate a fusion reaction. Another possible use is the so called Radiation Pressure Acceleration mechanism, in which a high-intensity, circularly polarized laser is used to create a mono-energetic ion beam which could then be used for medical imaging and treatment, among other applications. For this latter application, it is important that the laser energy is transferred to the ions and not to the electrons. However the physics of such high energy-density laser-matter interactions is highly kinetic and non-linear, and presently not fully understood. In this dissertation, we use the Particle-in-Cell code OSIRIS \cite{Fonseca:2002, Hemker:1999} to explore the generation and transport of relativistic particle beams created by high intensity lasers focused onto solid density matter at normal incidence. To explore the generation of relativistic electrons by such interactions, we use primarily one-dimensional (1D) and two-dimensional (2D), and a few three-dimensional simulations (3D). We initially examine the idealized case of normal incidence of relatively short, plane-wave lasers on flat, sharp interfaces. We find that in 1D the results are highly dependent on the initial temperature of the plasma, with significant absorption into relativistic electrons only possible when the temperature is high in the direction parallel to the electric field of the laser. In multi-dimensions, absorption into relativistic electrons arises independent of the initial temperature for both fixed and mobile ions, although the absorption is higher for mobile ions. In most cases however, absorption remains at $10's$ of percent, and as such a standing wave structure from the incoming and reflected wave is setup in front of the plasma surface. The peak momentum of the accelerated electrons is found to be $2 a_0 m_e c$, where $a_0 \equiv e A_0/m_e c^2$ is the normalized vector potential of the laser in vacuum, $e$ is the electron charge, $m_e$ is the electron mass, and $c$ is the speed of light. We consider cases for which $a_0>1$. We therefore call this the $2 a_0$ acceleration process. Using particle tracking, we identify the detailed physics behind the $2 a_0$ process and find it is related to the standing wave structure of the fields. We observe that the particles which gain energy do so by interacting with the laser electric field within a quarter wavelength of the surface where it is at an anti-node (it is a node at the surface). We find that only particles with high initial momentum -- in particular high transverse momentum -- are able to navigate through the laser magnetic field as its magnitude decreases in time each half laser cycle (it is an anti-node at the surface) to penetrate a quarter wavelength into the vacuum where the laser electric field is large. For a circularly polarized laser the magnetic field amplitude never decreases at the surface, instead its direction simply rotates. This prevents electrons from leaving the plasma and they therefore cannot gain energy from the electric field. For pulses with longer durations ($\gtrsim 250fs$), or for plasmas which do not have initially sharp interfaces, we discover that in addition to the $2 a_0$ acceleration at the surface, relativistic particles are also generated in an underdense region in front of the target. These particles have energies without a sharp upper bound. Although accelerating these particles removes energy from the incoming laser, and although the surface of the plasma does not stay perfectly flat and so the standing wave structure becomes modified, we find in most cases, the $2 a_0$ acceleration mechanism occurs similarly at the surface and that it still dominates the overall absorption of the laser. To explore the generation of relativistic electrons at a solid surface and transport of the heat flux of these electrons in cold or warm dense matter, we compare OSIRIS simulations with results from an experiment performed on the OMEGA laser system at the University of Rochester. In that experiment, a thin layer of gold placed on a slab of plastic is illuminated by an intense laser. A greater than order-of-magnitude decrease in the fluence of hot electrons is observed when those electrons are transported through a plasma created from a shock-heated plastic foam, as compared to transport through cold matter (unshocked plastic foam) at somewhat higher density. Our simulations indicate two reasons for the experimental result, both related to the magnetic field. The primary effect is the generation of a collimating B-field around the electron beam in the cold plastic foam, caused by the resistivity of the plastic. We use a Monte Carlo collision algorithm implemented in OSIRIS to model the experiment. The incoming relativistic electrons generate a return current. This generates a resistive electric field which then generates a magnetic field from Faraday's law. This magnetic field collimates the forward moving relativistic electrons. The collisionality of both the plastic and the gold are likely to be greater in the experiment than the 2D simulations where we used a lower density for the gold (to make the simulations possible) which heats up more. In addition, the use of 2D simulations also causes the plastic to heat up more than expected. We compensated for this by increasing the collisionality of the plasma in the simulations and this led to better agreement. The second effect is the growth of a strong, reflecting B-field at the edge of the plastic region in the shock heated material, created by the convective transport of this field back towards the beam source due to the neutralizing return current. Both effects appear to be caused primarily by the difference is density in the two cases. Owing to its higher heat capacity, the higher density material does not heat up as much from the heat flux coming from the gold, which leads to a larger resistivity. Lastly, we explored a numerical effect which has particular relevance to these simulations, due to their high energy and plasma densities. This effect is caused by the use of macro particles (which represent many real particles) which have the correct charge to mass ratio but higher charge. Therefore, any physics of a single charge that scales as $q^2/m$ will be artificially high. Physics that involves scales smaller than the macro-particle size can be mitigated through the use of finite size particles. However, for relativistic particles the spatial scale that matters is the skin depth and the cell sizes and particle sizes are both smaller than this. This allows the wakes created by these particles to be artificially high which causes them to slow down much faster than a single electron. We studied this macro-particle stopping power theoretically and in OSIRIS simulations. We also proposed a solution in which particles are split in to smaller particles as they gain energy. We call this effect Macro Particle Stopping. Although this effect can be mitigated by using more particles, this is not always computationally efficient. We show how it can also be mitigated by using high-order particle shapes, and/or by using a particle-splitting method which reduces the charge of only the most energetic electrons.