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{{short description|Charged particle acceleration technique}}
'''Plasma acceleration''' is a technique for accelerating ]s, such as ]s, ]s and ]s, using an ] associated with an ].
'''Plasma acceleration''' is a technique for accelerating ]s, such as ]s or ]s, using the ] associated with ] or other high-] ] structures. These plasma acceleration structures are created using either ultra-short ] pulses or energetic particle beams that are matched to the ]. The technique offers a way to build affordable and compact ]s.


Once fully developed, the technology can replace many of the traditional accelerators with applications ranging from ] to medical and industrial applications. Medical applications include ] and ] light sources for diagnostics or ] and ] sources for ].
A plasma consists of positive and negative charged particles. When these particles of the plasma are displaced properly, a very high electric field will arise. Incoming charged particles can now use this high electric field to accelerate to relativistic speeds.


== History ==
When a ] pulse or an electron bunch goes through a ], an electron plasma wave arises in its trace, like a wake following a ship on the ocean. Since an electron plasma wave is a ], high-density and low-density regions of electrons appear periodically in which the ] of the plasma is broken. An electric field originating from the breakdown of the neutrality, which is referred to as a "wakefield," accelerates charged particles inside the plasma in the direction parallel to the propagation direction of the electron plasma wave.
The basic concepts of plasma acceleration and its possibilities were originally conceived by ] and ] of ] in 1979.<ref>{{cite journal |last1= Tajima |first1= T. |last2= Dawson |first2= J. M. |s2cid= 27150340 |year= 1979 |title= Laser Electron Accelerator |journal= Phys. Rev. Lett. |volume= 43 |issue= 4|pages= 267–270 |doi= 10.1103/PhysRevLett.43.267 |bibcode=1979PhRvL..43..267T}}</ref> The initial experimental designs for a "wakefield" accelerator were conceived at UCLA by ] et al.<ref>{{cite journal |last1= Joshi |first1= C. |last2= Mori |first2= W. B. |last3= Katsouleas |first3= T. |last4= Dawson |first4= J. M. |last5= Kindel |first5= J. M. |last6= Forslund |first6= D. W. |year= 1984 |title= Ultrahigh gradient particle acceleration by intense laser-driven plasma density waves |journal= Nature |volume= 311 |issue= 5986|pages= 525–529 |doi= 10.1038/311525a0 |bibcode= 1984Natur.311..525J|s2cid= 4361301 }}</ref>


The ] facility at the ] accelerated electrons to 2&nbsp;GeV over about 2&nbsp;cm (1.6×10<sup>21</sup> ]).<ref>{{cite journal | last1=Wang | first1=Xiaoming | last2=Zgadzaj | first2=Rafal | last3=Fazel | first3=Neil | last4=Li | first4=Zhengyan | last5=Yi | first5=S. A. | last6=Zhang | first6=Xi | last7=Henderson | first7=Watson | last8=Chang | first8=Y.-Y. | last9=Korzekwa | first9=R. | last10=Tsai | first10=H.-E. | last11=Pai | first11=C.-H. | last12=Quevedo | first12=H. | last13=Dyer | first13=G. | last14=Gaul | first14=E. | last15=Martinez | first15=M. | last16=Bernstein | first16=A. C. | last17=Borger | first17=T. | last18=Spinks | first18=M. | last19=Donovan | first19=M. | last20=Khudik | first20=V. | last21=Shvets | first21=G. | last22=Ditmire | first22=T. | last23=Downer | first23=M. C. | title=Quasi-monoenergetic laser-plasma acceleration of electrons to 2&nbsp;GeV | journal=Nature Communications | publisher=Springer Nature | volume=4 | issue=1 | pages=1988 | date=June 11, 2013 | issn=2041-1723 | doi=10.1038/ncomms2988 |pmid= 23756359|pmc= 3709475|bibcode= 2013NatCo...4.1988W |display-authors=1}}</ref> This record was broken (by more than twice) in 2014 by the scientists at the ] Center at the ], when they produced electron beams up to 4.25&nbsp;GeV.<ref>{{cite journal | last1=Leemans | first1=W. P. | last2=Gonsalves | first2=A. J. | last3=Mao | first3=H.-S. | last4=Nakamura | first4=K. | last5=Benedetti | first5=C. | last6=Schroeder | first6=C. B. | last7=Tóth | first7=Cs. | last8=Daniels | first8=J. | last9=Mittelberger | first9=D. E. | last10=Bulanov | first10=S. S. | last11=Vay | first11=J.-L. | last12=Geddes | first12=C. G. R. | last13=Esarey | first13=E. | title=Multi-GeV Electron Beams from Capillary-Discharge-Guided Subpetawatt Laser Pulses in the Self-Trapping Regime | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=113 | issue=24 | pages=245002 | date=December 8, 2014 | issn=0031-9007 | doi=10.1103/physrevlett.113.245002 |display-authors=1|bibcode= 2014PhRvL.113x5002L |pmid=25541775| doi-access=free }}</ref>
Plasma acceleration is categorized into several types according to how the electron plasma wave is formed: plasma wakefield acceleration (PWFA), laser wakefield acceleration (LWFA), laser beat-wave acceleration (LBWA), and self-modulated laser wakefield acceleration (SMLWFA). In PWFA, an electron plasma wave is formed by an electron bunch. In LWFA, a laser pulse is introduced to form an electron plasma wave. In LBWA, an electron plasma wave arises based on different frequency generation of two laser pulses. And in SMLWFA, the formation of an electron plasma wave is achieved by a laser pulse modulated by ] instability.


In late 2014, researchers from ] using the Facility for Advanced Accelerator Experimental Tests (FACET) published proof of the viability of plasma acceleration technology. It was shown to be able to achieve 400 to 500 times higher energy transfer compared to a general linear accelerator design.<ref>{{cite journal | last1=Litos | first1=M. | last2=Adli | first2=E. | last3=An | first3=W. | last4=Clarke | first4=C. I. | last5=Clayton | first5=C. E. | last6=Corde | first6=S. | last7=Delahaye | first7=J. P. | last8=England | first8=R. J. | last9=Fisher | first9=A. S. | last10=Frederico | first10=J. | last11=Gessner | first11=S. | last12=Green | first12=S. Z. | last13=Hogan | first13=M. J. | last14=Joshi | first14=C. | last15=Lu | first15=W. | last16=Marsh | first16=K. A. | last17=Mori | first17=W. B. | last18=Muggli | first18=P. | last19=Vafaei-Najafabadi | first19=N. | last20=Walz | first20=D. | last21=White | first21=G. | last22=Wu | first22=Z. | last23=Yakimenko | first23=V. | last24=Yocky | first24=G. | title=High-efficiency acceleration of an electron beam in a plasma wakefield accelerator | journal=Nature | publisher=Springer Nature | volume=515 | issue=7525 | year=2014 | issn=0028-0836 | doi=10.1038/nature13882 | pages=92–95|display-authors=1|bibcode= 2014Natur.515...92L |pmid=25373678| osti=1463003 | s2cid=4469182 | url=https://www.osti.gov/biblio/1463003 }}</ref><ref>{{cite web |url=https://www6.slac.stanford.edu/news/2014-11-05-researchers-hit-milestone-accelerating-particles-plasma.aspx |title=Researchers Hit Milestone in Accelerating Particles with Plasma |publisher=SLAC National Accelerator Laboratory |date=November 5, 2014}}</ref>
]


A proof-of-principle plasma wakefield accelerator experiment using a 400&nbsp;GeV proton beam from the ] is currently operating at ].<ref>{{cite journal | last1=Assmann | first1=R. | last2=Mandry | first2=S. R. | last3=Öz | first3=E. | last4=Fonseca | first4=R. A. | last5=Moschuering | first5=N. | last6=Trines | first6=R. M. G. N. | last7=Gschwendtner | first7=E. | last8=Huang | first8=C. | last9=Bracco | first9=C. | last10=Reimann | first10=O. | last11=Butterworth | first11=A. | last12=McKenzie | first12=J. W. | last13=Lotov | first13=K. | last14=Tarkeshian | first14=R. | last15=Pukhov | first15=A. | last16=Sosedkin | first16=A. | last17=Jolly | first17=S. | last18=Cipiccia | first18=S. | last19=Vieira | first19=J. | last20=Machacek | first20=J. | last21=Buttenschön | first21=B. | last22=Gross | first22=M. | last23=Bingham | first23=R. | last24=Norreys | first24=P. A. | last25=Shaposhnikova | first25=E. | last26=Ruhl | first26=H. | last27=Holloway | first27=J. | last28=Feldbaumer | first28=E. | last29=Tückmantel | first29=T. | last30=Militsyn | first30=B. L. | last31=Jaroszynski | first31=D. | last32=Chattopadhyay | first32=S. | last33=Bohl | first33=T. | last34=Meddahi | first34=M. | last35=Caldwell | first35=A. | last36=Petrenko | first36=A. | last37=Muggli | first37=P. | last38=Najmudin | first38=Z. | last39=Lopes | first39=N. | last40=Wing | first40=M. | last41=Pardons | first41=A. | last42=Goddard | first42=B. | last43=Kempkes | first43=P. | last44=Grulke | first44=O. | last45=Vincke | first45=H. | last46=Silva | first46=L. O. | last47=Noakes | first47=T. C. Q. | last48=Xia | first48=G. | last49=Rieger | first49=K. | title=Proton-driven plasma wakefield acceleration: a path to the future of high-energy particle physics | journal=Plasma Physics and Controlled Fusion | volume=56 | issue=8 | pages=084013 | issn=1361-6587 | doi=10.1088/0741-3335/56/8/084013 | url=http://bib-pubdb1.desy.de/record/205163 | access-date=October 13, 2018 |bibcode= 2014PPCF...56h4013A|arxiv=1401.4823|display-authors=1| year=2014 | s2cid=62802109 }}</ref> The experiment, named ], started experiments at the end of 2016.<ref>{{cite web|title=AWAKE: Making waves in accelerator technology|url=https://home.cern/about/updates/2016/12/awake-making-waves-accelerator-technology|accessdate=20 July 2017}}</ref>
In a plasma wakefield accelerator, the wake is created when the space-charge force associated with the drive particles displaces the plasma electrons. The plasma ions, which are far more massive than the plasma electrons, remain stationary during the time scale of the beam passing through the plasma. Once expelled, the plasma electrons witness the space charge field of the ion column and are pulled back toward the beam axis, which results in a plasma electron density spike behind the center of the bunch (see below). The electric field associated with the density spike accelerates the particles at the back of the electron bunch.


In August 2020 scientists reported the achievement of a milestone in the development of laser-plasma accelerators and demonstrate their longest stable operation of 30 hours.<ref>{{cite news |title=World record: Plasma accelerator operates right around the clock |url=https://phys.org/news/2020-08-world-plasma-clock.html |accessdate=6 September 2020 |work=phys.org |language=en}}</ref><ref>{{cite news |title=Rekord: Längster Lauf eines Plasmabeschleunigers |url=https://www.scinexx.de/news/technik/rekord-laengster-lauf-eines-plasmabeschleunigers/ |accessdate=6 September 2020 |work=scinexx {{!}} Das Wissensmagazin |date=21 August 2020 |language=de-DE}}</ref><ref>{{cite news |title=Important Milestone Reached on the Road to Future Particle Accelerators |url=https://www.azom.com/news.aspx?newsID=54456 |accessdate=6 September 2020 |work=AZoM.com |date=20 August 2020 |language=en}}</ref><ref>{{cite news |title=Plasma accelerators could overcome size limitations of Large Hadron Collider |url=https://phys.org/news/2018-07-plasma-size-limitations-large-hadron.html |accessdate=6 September 2020 |work=phys.org |language=en}}</ref><ref>{{cite journal |last1=Maier |first1=Andreas R. |last2=Delbos |first2=Niels M. |last3=Eichner |first3=Timo |last4=Hübner |first4=Lars |last5=Jalas |first5=Sören |last6=Jeppe |first6=Laurids |last7=Jolly |first7=Spencer W. |last8=Kirchen |first8=Manuel |last9=Leroux |first9=Vincent |last10=Messner |first10=Philipp |last11=Schnepp |first11=Matthias |last12=Trunk |first12=Maximilian |last13=Walker |first13=Paul A. |last14=Werle |first14=Christian |last15=Winkler |first15=Paul |title=Decoding Sources of Energy Variability in a Laser-Plasma Accelerator |journal=Physical Review X |date=18 August 2020 |volume=10 |issue=3 |pages=031039 |doi=10.1103/PhysRevX.10.031039 |bibcode=2020PhRvX..10c1039M |doi-access=free }} ] Text and images are available under a .</ref>
The concept of plasma acceleration was first proposed by Toshiki Tajima and John Dawson in a theoretical article published in ]. The first experimental demonstration of wakefield acceleration, which was performed with PWFA, was reported by a research group at ] in ].


==Concept==
The advantage of plasma acceleration is that its acceleration field is much stronger than that of conventional radio-frequency (RF) ]. In RF accelerators, the acceleration field has an upper limit determined by the threshold for ] of the acceleration tube. Therefore, to obtain high-energy electrons or ions, a long acceleration length is inevitably required, resulting in huge sizes for accelerator facilities. On the other hand, plasma acceleration, in which the acceleration field is generated in plasma, achieves an acceleration field several orders of magnitude stronger than with RF accelerators. It is hoped that a compact particle accelerator can be created based on plasma acceleration techniques or accelerators for much higher energy can be built, if long accelerators are realizable with an accelerating field of 10 GeV/m.


=== Wakefield acceleration ===
==Formula==
A plasma consists of a fluid of positive and negative charged particles, generally created by heating or photo-ionizing (direct / tunneling / multi-photon / barrier-suppression) a dilute gas. Under normal conditions the plasma will be macroscopically neutral (or quasi-neutral), an equal mix of ]s and ]s in equilibrium. However, if a strong enough external electric or electromagnetic field is applied, the plasma electrons, which are very light in comparison to the background ions (by a factor of 1836), will separate spatially from the massive ions creating a charge imbalance in the perturbed region. A particle injected into such a plasma would be accelerated by the charge separation field, but since the magnitude of this separation is generally similar to that of the external field, apparently nothing is gained in comparison to a conventional system that simply applies the field directly to the particle. But, the plasma medium acts as the most efficient transformer (currently known) of the transverse field of an electromagnetic wave into longitudinal fields of a plasma wave. In existing accelerator technology various appropriately designed materials are used to convert from transverse propagating extremely intense fields into longitudinal fields that the particles can get a kick from. This process is achieved using two approaches: standing-wave structures (such as resonant cavities) or traveling-wave structures such as disc-loaded waveguides etc. But, the limitation of materials interacting with higher and higher fields is that they eventually get destroyed through ionization and breakdown. Here the plasma accelerator science provides the breakthrough to generate, sustain, and exploit the highest fields ever produced in the laboratory.
According to the acceleration gradient for a linear plasma wave is:


]
<math>E = c \cdot \sqrt{\frac{m_e \cdot \rho}{\epsilon_0}}</math>


The acceleration gradient produced by a plasma wake is in the order of the wave breaking field, which is
In this equation, <math>E</math> is the ], <math>c</math> is the ] in vacuum, <math>m_e</math> is the mass of the ], <math>\rho</math> is the plasma density, and <math>\epsilon_0</math> is the ].
:<math>E_0 = \sqrt{\frac{m_e n_e c^2}{\varepsilon_0}}.</math>

In this equation, <math>E_0</math> is the ], <math>c</math> is the ] in vacuum, <math>m_e</math> is the mass of the ], <math>n_e</math> is the plasma electron density (in particles per unit volume), and <math>\varepsilon_0</math> is the ].

What makes the system useful is the possibility of introducing waves of very high charge separation that propagate through the plasma similar to the traveling-wave concept in the conventional accelerator. The accelerator thereby phase-locks a particle bunch on a wave and this loaded space-charge wave accelerates them to higher velocities while retaining the bunch properties. Currently, plasma wakes are excited by appropriately shaped ] pulses or electron bunches. Plasma electrons are driven out and away from the center of wake by the ] or the electrostatic fields from the exciting fields (electron or laser). Plasma ions are too massive to move significantly and are assumed to be stationary at the time-scales of plasma electron response to the exciting fields. As the exciting fields pass through the plasma, the plasma electrons experience a massive attractive force back to the center of the wake by the positive plasma ions chamber, bubble or column that have remained positioned there, as they were originally in the unexcited plasma. This forms a full wake of an extremely high longitudinal (accelerating) and transverse (focusing) electric field. The positive charge from ions in the charge-separation region then creates a huge gradient between the back of the wake, where there are many electrons, and the middle of the wake, where there are mostly ions. Any electrons in between these two areas will be accelerated (in self-injection mechanism). In the external bunch injection schemes the electrons are strategically injected to arrive at the evacuated region during maximum excursion or expulsion of the plasma electrons.

A beam-driven wake can be created by sending a relativistic proton or electron bunch into an appropriate plasma or gas.<ref>{{cite journal |last1= Caldwell |first1= A. |year= 2016 |title= Path to AWAKE: Evolution of the concept |url= http://strathprints.strath.ac.uk/56629/ |journal= Nuclear Instruments and Methods in Physics Research Section A |volume= 829 |pages= 3–16 |doi= 10.1016/j.nima.2015.12.050 |arxiv= 1511.09032 |bibcode= 2016NIMPA.829....3C|hdl= 11858/00-001M-0000-002B-2685-0 |s2cid= 42463366 }}</ref> In some cases, the gas can be ionized by the electron bunch, so that the electron bunch both creates the plasma and the wake. This requires an electron bunch with relatively high charge and thus strong fields. The high fields of the electron bunch then push the plasma electrons out from the center, creating the wake.

Similar to a beam-driven wake, a laser pulse can be used to excite the plasma wake. As the pulse travels through the plasma, the electric field of the light separates the electrons and nucleons in the same way that an external field would.

If the fields are strong enough, all of the ionized plasma electrons can be removed from the center of the wake: this is known as the "blowout regime". Although the particles are not moving very quickly during this period, macroscopically it appears that a "bubble" of charge is moving through the plasma at close to the speed of light. The bubble is the region cleared of electrons that is thus positively charged, followed by the region where the electrons fall back into the center and is thus negatively charged. This leads to a small area of very strong potential gradient following the laser pulse.

In the linear regime, plasma electrons aren't completely removed from the center of the wake. In this case, the linear plasma wave equation can be applied. However, the wake appears very similar to the blowout regime, and the physics of acceleration is the same.

It is this "wakefield" that is used for particle acceleration. A particle injected into the plasma near the high-density area will experience an acceleration toward (or away) from it, an acceleration that continues as the wakefield travels through the column, until the particle eventually reaches the speed of the wakefield. Even higher energies can be reached by injecting the particle to travel across the face of the wakefield, much like a ] can travel at speeds much higher than the wave they surf on by traveling across it. Accelerators designed to take advantage of this technique have been referred to colloquially as "surfatrons".

The wakefield acceleration can be categorized into several types according to how the electron plasma wave is formed:
*''plasma wakefield acceleration'' '''(PWFA)''': The electron plasma wave is formed by an electron or proton bunch.
*''laser wakefield acceleration'' '''(LWFA)''': A laser pulse is introduced to form an electron plasma wave.
*''laser beat-wave acceleration'' '''(LBWA)''': The electron plasma wave arises based on different frequency generation of two laser pulses. The "Surfatron" is an improvement on this technique.<ref>{{cite journal |last1= Katsouleas |first1= T. |last2= Dawson |first2= J. M. |year= 1983 |title= A Plasma Wave Accelerator - Surfatron I |journal= IEEE Trans. Nucl. Sci. |volume= 30 |issue= 4|pages= 3241–3243 |doi= 10.1109/TNS.1983.4336628 |bibcode= 1983ITNS...30.3241K|s2cid= 41359956 }}</ref>
*''self-modulated laser wakefield acceleration'' '''(SMLWFA)''': The formation of an electron plasma wave is achieved by a laser pulse modulated by ] instability.
Some experiments are:<ref>{{Cite web |last=Garisto |first=Daniel |date=2019-03-14 |title=The potential of plasma wakefield acceleration {{!}} symmetry magazine |url=https://www.symmetrymagazine.org/article/the-potential-of-plasma-wakefield-acceleration?language_content_entity=und |access-date=2024-03-22 |website=www.symmetrymagazine.org |language=en}}</ref>
{| class="wikitable"
|+
!Type of acceleration
!Experiments
|-
|Laser wakefield acceleration
|BELLA, TREX, CLF, LUX
|-
|Plasma wakefield acceleration using electrons
|FACET, ,
|-
|Plasma wakefield acceleration using positrons
|FACET, FACET II
|-
|Plasma wakefield acceleration using protons
|]
|}

=== Target normal sheath acceleration ===
Laser–solid-target-based ion acceleration has become an active area of research, especially since the discovery of the target normal sheath acceleration (TNSA).<ref>{{Cite journal|last1=Snavely|first1=R. A.|last2=Key|first2=M. H.|last3=Hatchett|first3=S. P.|last4=Cowan|first4=T. E.|last5=Roth|first5=M.|last6=Phillips|first6=T. W.|last7=Stoyer|first7=M. A.|last8=Henry|first8=E. A.|last9=Sangster|first9=T. C.|last10=Singh|first10=M. S.|last11=Wilks|first11=S. C.|date=2000-10-02|title=Intense High-Energy Proton Beams from Petawatt-Laser Irradiation of Solids|url=https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.85.2945|journal=Physical Review Letters|volume=85|issue=14|pages=2945–2948|doi=10.1103/physrevlett.85.2945|pmid=11005974|bibcode=2000PhRvL..85.2945S|issn=0031-9007}}</ref> This new scheme offers further improvements in ],<ref>{{Cite journal|date=2002-07-01|title=Oncological hadrontherapy with laser ion accelerators|url=https://www.sciencedirect.com/science/article/abs/pii/S0375960102005212|journal=Physics Letters A|language=en|volume=299|issue=2–3|pages=240–247|doi=10.1016/S0375-9601(02)00521-2|issn=0375-9601|last1=Bulanov|first1=S.V|last2=Esirkepov|first2=T.Zh|last3=Khoroshkov|first3=V.S|last4=Kuznetsov|first4=A.V|last5=Pegoraro|first5=F.|bibcode=2002PhLA..299..240B}}</ref> ]<ref>{{Cite journal|last1=Roth|first1=M.|last2=Cowan|first2=T. E.|last3=Key|first3=M. H.|last4=Hatchett|first4=S. P.|last5=Brown|first5=C.|last6=Fountain|first6=W.|last7=Johnson|first7=J.|last8=Pennington|first8=D. M.|last9=Snavely|first9=R. A.|last10=Wilks|first10=S. C.|last11=Yasuike|first11=K.|date=2001-01-15|title=Fast Ignition by Intense Laser-Accelerated Proton Beams|url=https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.86.436|journal=Physical Review Letters|volume=86|issue=3|pages=436–439|doi=10.1103/physrevlett.86.436|pmid=11177849|bibcode=2001PhRvL..86..436R|issn=0031-9007}}</ref> and sources for fundamental research.<ref name=":0">{{Citation|last1=Roth|first1=Markus|title=Ion Acceleration: TNSA|date=2013|url=https://doi.org/10.1007/978-3-319-00038-1_12|work=Laser-Plasma Interactions and Applications|pages=303–350|editor-last=McKenna|editor-first=Paul|series=Scottish Graduate Series|place=Heidelberg|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-319-00038-1_12|isbn=978-3-319-00038-1|access-date=2021-06-10|last2=Schollmeier|first2=Marius|bibcode=2013lpia.book..303R|editor2-last=Neely|editor2-first=David|editor3-last=Bingham|editor3-first=Robert|editor4-last=Jaroszynski|editor4-first=Dino}}</ref> Nonetheless, the maximum energies achieved so far with this scheme are in the order of 100 MeV energies.<ref>{{Cite journal|last1=Higginson|first1=A.|last2=Gray|first2=R. J.|last3=King|first3=M.|last4=Dance|first4=R. J.|last5=Williamson|first5=S. D. R.|last6=Butler|first6=N. M. H.|last7=Wilson|first7=R.|last8=Capdessus|first8=R.|last9=Armstrong|first9=C.|last10=Green|first10=J. S.|last11=Hawkes|first11=S. J.|date=2018-02-20|title=Near-100 MeV protons via a laser-driven transparency-enhanced hybrid acceleration scheme|journal=Nature Communications|language=en|volume=9|issue=1|pages=724|doi=10.1038/s41467-018-03063-9|pmid=29463872|issn=2041-1723|pmc=5820283|bibcode=2018NatCo...9..724H}}</ref>

The main laser-solid acceleration scheme is Target Normal Sheath Acceleration, TNSA as it is usually referred as. TNSA like other laser based acceleration techniques is not capable of directly accelerating the ions. Instead it is a multi-step process consisting of several stages each with its associated difficulty to model mathematically. For this reason, so far there exists no perfect theoretical model capable of producing quantitative predictions for the TNSA mechanism.<ref name=":0" /> ] simulations are usually employed to efficiently achieve predictions.

The scheme employs a solid target that interacts firstly with the laser prepulse, this ionises the target turning it into a plasma and causing a pre-expansion of the target front. Which produces an underdense plasma region at the front of the target, the so-called preplasma. Once the main laser pulse arrives at the target front it will then propagate through this underdense region and be reflected from the front surface of the target propagating back through the preplasma. Throughout this process the laser has heated up the electrons in the underdense region and accelerated them via stochastic heating.<ref>{{Cite journal|date=2005-06-15|title=Stochastic heating in ultra high intensity laser-plasma interaction|url=https://www.sciencedirect.com/science/article/abs/pii/S0167278905001375|journal=Physica D: Nonlinear Phenomena|language=en|volume=206|issue=1–2|pages=1–31|doi=10.1016/j.physd.2005.04.017|issn=0167-2789|last1=Bourdier|first1=A.|last2=Patin|first2=D.|last3=Lefebvre|first3=E.|s2cid=20452990}}</ref> This heating process is incredibly important, producing a high temperature electron populations is key for the next steps of the process. The importance of the preplasma in the electron heating process has recently been studied both theoretically and experimentally showing how longer preplasmas lead to stronger electron heating and an enhancement in TNSA.<ref>{{Cite journal|last1=Gizzi|first1=Leonida A.|last2=Boella|first2=Elisabetta|last3=Labate|first3=Luca|last4=Baffigi|first4=Federica|last5=Bilbao|first5=Pablo J.|last6=Brandi|first6=Fernando|last7=Cristoforetti|first7=Gabriele|last8=Fazzi|first8=Alberto|last9=Fulgentini|first9=Lorenzo|last10=Giove|first10=Dario|last11=Koester|first11=Petra|date=2021-07-02|title=Enhanced laser-driven proton acceleration via improved fast electron heating in a controlled pre-plasma|journal=Scientific Reports|language=en|volume=11|issue=1|pages=13728|pmid=34215775 | doi=10.1038/s41598-021-93011-3| arxiv=2106.00814 |issn=2045-2322|pmc=8253820|bibcode=2021NatSR..1113728G }}</ref> The hot electrons propagate through the solid target and exit it through the rear end. In doing so, the electrons produce an incredibly strong electric field, in the order of TV/m,<ref name=":0" /> through charge separation. This electric field, also referred to as the sheath field due to its resemblance with the shape of a sheath from a sword, is responsible for the acceleration of the ions. On the rear face of the target there is a small layer of contaminants (usually light hydrocarbons and water vapor). These contaminants are ionised by the strong electric field generated by the hot electrons and then accelerated. Which leads to an energetic ion beam and completes the acceleration process.

Responsible for the spiky, fast ion front of the expanding plasma is an ion wave breaking process that takes place in the initial phase of the evolution and is described by the ].<ref>Ch. Sack and H.Schamel, Plasma expansion into vacuum - A hydrodynamic approach, Phys. Reports 156 (1987) 311-395 | doi:10.1016/0370-1573(87)90039-1|</ref>

==Comparison with RF acceleration==

The advantage of plasma acceleration is that its acceleration field can be much stronger than that of conventional radio-frequency (RF) ]. In RF accelerators, the field has an upper limit determined by the threshold for ] of the acceleration tube. This limits the amount of acceleration over any given length, requiring very long accelerators to reach high energies. In contrast, the maximum field in a plasma is defined by mechanical qualities and turbulence, but is generally several orders of magnitude stronger than with RF accelerators. It is hoped that a compact particle accelerator can be created based on plasma acceleration techniques or accelerators for much higher energy can be built, if long accelerators are realizable with an accelerating field of 10 GV/m.

Current experimental devices show accelerating gradients several orders of magnitude better than current particle accelerators over very short distances, and about one order of magnitude better (1 ]/m<ref>{{cite conference | last1=Katsouleas | first1=T. | last2=Lee | first2=S. | last3=Chattopadhyay | first3=S. | last4=Leemand | first4=W. | last5=Assmann | first5=R. | last6=Chen | first6=P. | last7=Decker | first7=F.J. | last8=Iverson | first8=R. | last9=Kotseroglou | first9=T. | last10=Raimondi | first10=P. | last11=Raubenheimer | first11=T. | last12=Eokni | first12=S. | last13=Siemann | first13=R.H. | last14=Walz | first14=D. | last15=Whittum | first15=D. | last16=Clayton | first16=C. | last17=Joshi | first17=C. | last18=Marsh | first18=K. | last19=Mori | first19=W. | last20=Wang | first20=G. | title=Proceedings of the 1997 Particle Accelerator Conference (Cat. No.97CH36167) | chapter=A proposal for a 1&nbsp;GeV plasma-wakefield acceleration experiment at SLAC | year=1998 | volume=1 | pages=687–689 | publisher=IEEE | isbn=0-7803-4376-X | doi=10.1109/pac.1997.749806 |display-authors=1 |chapter-url=https://www.researchgate.net/publication/224275850| citeseerx=10.1.1.389.1097 }}</ref> vs 0.1&nbsp;GeV/m for an RF accelerator<ref>{{cite journal | last1=Takeda | first1=S | last2=Kuroda | first2=S | last3=Kimura | first3=Y | last4=Sakai | first4=H | last5=Odagiri | first5=J | last6=Ishihara | first6=N | last7=Araki | first7=S | last8=Suetake | first8=M | last9=Akemoto | first9=M | last10=Yamaoka | first10=Y | last11=Takata | first11=K | last12=Yoshioka | first12=M | last13=Akiyama | first13=H | last14=Akai | first14=K | last15=Hayano | first15=H | last16=Kubo | first16=T | last17=Otake | first17=Y | last18=Takeuchi | first18=Y | last19=Kawamoto | first19=T | last20=Urakawa | first20=J | last21=Shidara | first21=T | last22=Matsumoto | first22=H | last23=Takashima | first23=T | last24=Yokoya | first24=K | last25=Shintake | first25=T | last26=Mizuno | first26=H | last27=Higo | first27=T | last28=Kurokawa | first28=S | last29=Kobayashi | first29=H | last30=Naito | first30=T | last31=Yamamoto | first31=N | last32=Yoshida | first32=M | title=Electron Linac Of Test Accelerator Facility For Linear collider | journal=Part. Accel. | volume=30 | date=November 27, 2014 | url=https://core.ac.uk/download/pdf/44197249.pdf | access-date=October 13, 2018 | pages=153–159 |display-authors=1}}</ref>) at the one meter scale.

For example, an experimental laser plasma accelerator at ] accelerates electrons to 1&nbsp;GeV over about 3.3&nbsp;cm (5.4×10<sup>20</sup> g<sub>n</sub>),<ref>{{cite journal | last1=Leemans | first1=W. P. | last2=Nagler | first2=B. | last3=Gonsalves | first3=A. J. | last4=Tóth | first4=Cs. | last5=Nakamura | first5=K. | last6=Geddes | first6=C. G. R. | last7=Esarey | first7=E. | last8=Schroeder | first8=C. B. | last9=Hooker | first9=S. M. | title=GeV electron beams from a centimetre-scale accelerator | journal=Nature Physics | publisher=Springer Nature | volume=2 | issue=10 | date=September 24, 2006 | issn=1745-2473 | doi=10.1038/nphys418 | pages=696–699|display-authors= 1|bibcode= 2006NatPh...2..696L |doi-access=free }}</ref> and one conventional accelerator (highest electron energy accelerator) at ] requires 64 m to reach the same energy. Similarly, using plasmas an energy gain of more than 40 ] was achieved using the SLAC SLC beam (42&nbsp;GeV) in just 85&nbsp;cm using a plasma wakefield accelerator (8.9×10<sup>20</sup> g<sub>n</sub>).<ref>{{cite journal | last1=Blumenfeld | first1=Ian | last2=Clayton | first2=Christopher E. | last3=Decker | first3=Franz-Josef | last4=Hogan | first4=Mark J. | last5=Huang | first5=Chengkun | last6=Ischebeck | first6=Rasmus | last7=Iverson | first7=Richard | last8=Joshi | first8=Chandrashekhar | last9=Katsouleas | first9=Thomas | last10=Kirby | first10=Neil | last11=Lu | first11=Wei | last12=Marsh | first12=Kenneth A. | last13=Mori | first13=Warren B. | last14=Muggli | first14=Patric | last15=Oz | first15=Erdem | last16=Siemann | first16=Robert H. | last17=Walz | first17=Dieter | last18=Zhou | first18=Miaomiao | title=Energy doubling of 42&nbsp;GeV electrons in a metre-scale plasma wakefield accelerator | journal=Nature | publisher=Springer Nature | volume=445 | issue=7129 | year=2007 | issn=0028-0836 | doi=10.1038/nature05538 | pages=741–744|display-authors= 1|pmid= 17301787|bibcode= 2007Natur.445..741B| s2cid=4334568 }}</ref>

== Application ==
In the framework of ] which is the Framework Programmes for Research and Technological Development the Conceptual Design Report<ref>{{Cite journal |last=Assmann |first=R.W. |last2=et. |first2=al. |date=2020 |title=EuPRAXIA Conceptual Design Report |url=https://link.springer.com/article/10.1140/epjst/e2020-000127-8 |journal=Eur. Phys. J. Special Topics |volume=229 |pages=3675-4284 |doi=10.1140/epjst/e2020-000127-8|doi-access=free }}</ref> of project “(European Plasma Research Accelerator with eXcellence In Applications”) was worked out by 74 scientific institutes. To find out which will be the most suitable technology, laserdriven (laser wakefield acceleration, LWFA), electron beam-driven (plasma wakefield acceleration, PWFA) as well as hybrid (combining LWFA and PWFA) acceleration approaches are under consideration. The beam-driven plasma wakefield acceleration facility will be built in the ] National Laboratory of ] (LNF) near Rome in Italy. The second site of laser-driven (laser wakefield acceleration, LWFA) facility is however till undecided. Decision will be made in mid 2025.

==See also==
*]

==References==
{{Reflist}}
*{{cite journal |last1= Joshi |first1= C. |author-link= Chandrashekhar J. Joshi |year= 2006 |title= Plasma Accelerators |journal= Scientific American |volume= 294 |issue= 2|pages= 40–47 |doi=10.1038/scientificamerican0206-40 |pmid= 16478025 |bibcode= 2006SciAm.294b..40J}}
*{{cite journal |last1= Katsouleas |first1= T |year= 2004|title= Accelerator physics: Electrons hang ten on laser wake |journal= Nature |volume= 431 |issue= 7008|pages= 515–516 |doi= 10.1038/431515a |pmid= 15457239 |bibcode= 2004Natur.431..515K|s2cid= 11111762 }}
*{{cite journal |last1= Joshi |first1= C. |last2= Katsouleas |first2= T. |year= 2003 |title= Plasma accelerators at the energy frontier and on tabletops |journal= Physics Today |volume= 56 |issue= 6 |pages= 47–51 |doi= 10.1063/1.1595054 |bibcode= 2003PhT....56f..47J}}
*{{cite journal |last1= Joshi |first1= C. |last2= Malka |first2= V. |name-list-style=amp |date= 2010 |title= Focus on Laser- and Beam-Driven Plasma Accelerators |journal= ] |volume= 12|issue= 4|pages= 045003|doi= 10.1088/1367-2630/12/4/045003|doi-access= free }}


==External links== ==External links==
*
* http://home.fnal.gov/~carrigan/Accelerators/Accelerator_master.htm
*
* http://pbpl.physics.ucla.edu/Research/Experiments/Advanced_Accelerators/Plasma_Acceleration/PBWA/
* http://icfa-usa.jlab.org/archive/newsletter/icfa_bd_nl_12/node26.html


] ]
] ]

Latest revision as of 04:25, 16 December 2024

Charged particle acceleration technique

Plasma acceleration is a technique for accelerating charged particles, such as electrons or ions, using the electric field associated with electron plasma wave or other high-gradient plasma structures. These plasma acceleration structures are created using either ultra-short laser pulses or energetic particle beams that are matched to the plasma parameters. The technique offers a way to build affordable and compact particle accelerators.

Once fully developed, the technology can replace many of the traditional accelerators with applications ranging from high energy physics to medical and industrial applications. Medical applications include betatron and free-electron light sources for diagnostics or radiation therapy and proton sources for hadron therapy.

History

The basic concepts of plasma acceleration and its possibilities were originally conceived by Toshiki Tajima and John M. Dawson of UCLA in 1979. The initial experimental designs for a "wakefield" accelerator were conceived at UCLA by Chandrashekhar J. Joshi et al.

The Texas Petawatt laser facility at the University of Texas at Austin accelerated electrons to 2 GeV over about 2 cm (1.6×10 gn). This record was broken (by more than twice) in 2014 by the scientists at the BELLA Center at the Lawrence Berkeley National Laboratory, when they produced electron beams up to 4.25 GeV.

In late 2014, researchers from SLAC National Accelerator Laboratory using the Facility for Advanced Accelerator Experimental Tests (FACET) published proof of the viability of plasma acceleration technology. It was shown to be able to achieve 400 to 500 times higher energy transfer compared to a general linear accelerator design.

A proof-of-principle plasma wakefield accelerator experiment using a 400 GeV proton beam from the Super Proton Synchrotron is currently operating at CERN. The experiment, named AWAKE, started experiments at the end of 2016.

In August 2020 scientists reported the achievement of a milestone in the development of laser-plasma accelerators and demonstrate their longest stable operation of 30 hours.

Concept

Wakefield acceleration

A plasma consists of a fluid of positive and negative charged particles, generally created by heating or photo-ionizing (direct / tunneling / multi-photon / barrier-suppression) a dilute gas. Under normal conditions the plasma will be macroscopically neutral (or quasi-neutral), an equal mix of electrons and ions in equilibrium. However, if a strong enough external electric or electromagnetic field is applied, the plasma electrons, which are very light in comparison to the background ions (by a factor of 1836), will separate spatially from the massive ions creating a charge imbalance in the perturbed region. A particle injected into such a plasma would be accelerated by the charge separation field, but since the magnitude of this separation is generally similar to that of the external field, apparently nothing is gained in comparison to a conventional system that simply applies the field directly to the particle. But, the plasma medium acts as the most efficient transformer (currently known) of the transverse field of an electromagnetic wave into longitudinal fields of a plasma wave. In existing accelerator technology various appropriately designed materials are used to convert from transverse propagating extremely intense fields into longitudinal fields that the particles can get a kick from. This process is achieved using two approaches: standing-wave structures (such as resonant cavities) or traveling-wave structures such as disc-loaded waveguides etc. But, the limitation of materials interacting with higher and higher fields is that they eventually get destroyed through ionization and breakdown. Here the plasma accelerator science provides the breakthrough to generate, sustain, and exploit the highest fields ever produced in the laboratory.

Wake created by an electron beam in a plasma

The acceleration gradient produced by a plasma wake is in the order of the wave breaking field, which is

E 0 = m e n e c 2 ε 0 . {\displaystyle E_{0}={\sqrt {\frac {m_{e}n_{e}c^{2}}{\varepsilon _{0}}}}.}

In this equation, E 0 {\displaystyle E_{0}} is the electric field, c {\displaystyle c} is the speed of light in vacuum, m e {\displaystyle m_{e}} is the mass of the electron, n e {\displaystyle n_{e}} is the plasma electron density (in particles per unit volume), and ε 0 {\displaystyle \varepsilon _{0}} is the permittivity of free space.

What makes the system useful is the possibility of introducing waves of very high charge separation that propagate through the plasma similar to the traveling-wave concept in the conventional accelerator. The accelerator thereby phase-locks a particle bunch on a wave and this loaded space-charge wave accelerates them to higher velocities while retaining the bunch properties. Currently, plasma wakes are excited by appropriately shaped laser pulses or electron bunches. Plasma electrons are driven out and away from the center of wake by the ponderomotive force or the electrostatic fields from the exciting fields (electron or laser). Plasma ions are too massive to move significantly and are assumed to be stationary at the time-scales of plasma electron response to the exciting fields. As the exciting fields pass through the plasma, the plasma electrons experience a massive attractive force back to the center of the wake by the positive plasma ions chamber, bubble or column that have remained positioned there, as they were originally in the unexcited plasma. This forms a full wake of an extremely high longitudinal (accelerating) and transverse (focusing) electric field. The positive charge from ions in the charge-separation region then creates a huge gradient between the back of the wake, where there are many electrons, and the middle of the wake, where there are mostly ions. Any electrons in between these two areas will be accelerated (in self-injection mechanism). In the external bunch injection schemes the electrons are strategically injected to arrive at the evacuated region during maximum excursion or expulsion of the plasma electrons.

A beam-driven wake can be created by sending a relativistic proton or electron bunch into an appropriate plasma or gas. In some cases, the gas can be ionized by the electron bunch, so that the electron bunch both creates the plasma and the wake. This requires an electron bunch with relatively high charge and thus strong fields. The high fields of the electron bunch then push the plasma electrons out from the center, creating the wake.

Similar to a beam-driven wake, a laser pulse can be used to excite the plasma wake. As the pulse travels through the plasma, the electric field of the light separates the electrons and nucleons in the same way that an external field would.

If the fields are strong enough, all of the ionized plasma electrons can be removed from the center of the wake: this is known as the "blowout regime". Although the particles are not moving very quickly during this period, macroscopically it appears that a "bubble" of charge is moving through the plasma at close to the speed of light. The bubble is the region cleared of electrons that is thus positively charged, followed by the region where the electrons fall back into the center and is thus negatively charged. This leads to a small area of very strong potential gradient following the laser pulse.

In the linear regime, plasma electrons aren't completely removed from the center of the wake. In this case, the linear plasma wave equation can be applied. However, the wake appears very similar to the blowout regime, and the physics of acceleration is the same.

It is this "wakefield" that is used for particle acceleration. A particle injected into the plasma near the high-density area will experience an acceleration toward (or away) from it, an acceleration that continues as the wakefield travels through the column, until the particle eventually reaches the speed of the wakefield. Even higher energies can be reached by injecting the particle to travel across the face of the wakefield, much like a surfer can travel at speeds much higher than the wave they surf on by traveling across it. Accelerators designed to take advantage of this technique have been referred to colloquially as "surfatrons".

The wakefield acceleration can be categorized into several types according to how the electron plasma wave is formed:

  • plasma wakefield acceleration (PWFA): The electron plasma wave is formed by an electron or proton bunch.
  • laser wakefield acceleration (LWFA): A laser pulse is introduced to form an electron plasma wave.
  • laser beat-wave acceleration (LBWA): The electron plasma wave arises based on different frequency generation of two laser pulses. The "Surfatron" is an improvement on this technique.
  • self-modulated laser wakefield acceleration (SMLWFA): The formation of an electron plasma wave is achieved by a laser pulse modulated by stimulated Raman forward scattering instability.

Some experiments are:

Type of acceleration Experiments
Laser wakefield acceleration BELLA, TREX, CLF, LUX
Plasma wakefield acceleration using electrons FACET, FACET II, DESY FLASHForward
Plasma wakefield acceleration using positrons FACET, FACET II
Plasma wakefield acceleration using protons AWAKE

Target normal sheath acceleration

Laser–solid-target-based ion acceleration has become an active area of research, especially since the discovery of the target normal sheath acceleration (TNSA). This new scheme offers further improvements in hadrontherapy, fusion fast ignition and sources for fundamental research. Nonetheless, the maximum energies achieved so far with this scheme are in the order of 100 MeV energies.

The main laser-solid acceleration scheme is Target Normal Sheath Acceleration, TNSA as it is usually referred as. TNSA like other laser based acceleration techniques is not capable of directly accelerating the ions. Instead it is a multi-step process consisting of several stages each with its associated difficulty to model mathematically. For this reason, so far there exists no perfect theoretical model capable of producing quantitative predictions for the TNSA mechanism. Particle-in-Cell simulations are usually employed to efficiently achieve predictions.

The scheme employs a solid target that interacts firstly with the laser prepulse, this ionises the target turning it into a plasma and causing a pre-expansion of the target front. Which produces an underdense plasma region at the front of the target, the so-called preplasma. Once the main laser pulse arrives at the target front it will then propagate through this underdense region and be reflected from the front surface of the target propagating back through the preplasma. Throughout this process the laser has heated up the electrons in the underdense region and accelerated them via stochastic heating. This heating process is incredibly important, producing a high temperature electron populations is key for the next steps of the process. The importance of the preplasma in the electron heating process has recently been studied both theoretically and experimentally showing how longer preplasmas lead to stronger electron heating and an enhancement in TNSA. The hot electrons propagate through the solid target and exit it through the rear end. In doing so, the electrons produce an incredibly strong electric field, in the order of TV/m, through charge separation. This electric field, also referred to as the sheath field due to its resemblance with the shape of a sheath from a sword, is responsible for the acceleration of the ions. On the rear face of the target there is a small layer of contaminants (usually light hydrocarbons and water vapor). These contaminants are ionised by the strong electric field generated by the hot electrons and then accelerated. Which leads to an energetic ion beam and completes the acceleration process.

Responsible for the spiky, fast ion front of the expanding plasma is an ion wave breaking process that takes place in the initial phase of the evolution and is described by the Sack-Schamel equation.

Comparison with RF acceleration

The advantage of plasma acceleration is that its acceleration field can be much stronger than that of conventional radio-frequency (RF) accelerators. In RF accelerators, the field has an upper limit determined by the threshold for dielectric breakdown of the acceleration tube. This limits the amount of acceleration over any given length, requiring very long accelerators to reach high energies. In contrast, the maximum field in a plasma is defined by mechanical qualities and turbulence, but is generally several orders of magnitude stronger than with RF accelerators. It is hoped that a compact particle accelerator can be created based on plasma acceleration techniques or accelerators for much higher energy can be built, if long accelerators are realizable with an accelerating field of 10 GV/m.

Current experimental devices show accelerating gradients several orders of magnitude better than current particle accelerators over very short distances, and about one order of magnitude better (1 GeV/m vs 0.1 GeV/m for an RF accelerator) at the one meter scale.

For example, an experimental laser plasma accelerator at Lawrence Berkeley National Laboratory accelerates electrons to 1 GeV over about 3.3 cm (5.4×10 gn), and one conventional accelerator (highest electron energy accelerator) at SLAC requires 64 m to reach the same energy. Similarly, using plasmas an energy gain of more than 40 GeV was achieved using the SLAC SLC beam (42 GeV) in just 85 cm using a plasma wakefield accelerator (8.9×10 gn).

Application

In the framework of HORIZON 2020 which is the Framework Programmes for Research and Technological Development the Conceptual Design Report of EuPRAXIA project “(European Plasma Research Accelerator with eXcellence In Applications”) was worked out by 74 scientific institutes. To find out which will be the most suitable technology, laserdriven (laser wakefield acceleration, LWFA), electron beam-driven (plasma wakefield acceleration, PWFA) as well as hybrid (combining LWFA and PWFA) acceleration approaches are under consideration. The beam-driven plasma wakefield acceleration facility will be built in the INFN National Laboratory of Frascati (LNF) near Rome in Italy. The second site of laser-driven (laser wakefield acceleration, LWFA) facility is however till undecided. Decision will be made in mid 2025.

See also

References

  1. Tajima, T.; Dawson, J. M. (1979). "Laser Electron Accelerator". Phys. Rev. Lett. 43 (4): 267–270. Bibcode:1979PhRvL..43..267T. doi:10.1103/PhysRevLett.43.267. S2CID 27150340.
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