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Particle Acceleration

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Book cover Physics of Collisionless Shocks

Part of the book series: ISSI Scientific Report Series ((ISSI,volume 12))

Abstract

Shocks are believed to be the primary accelerator of charged particles in space. This chapter reviews the basic theory and observations in near-Earth space. It discusses the Fermi and diffuse ion acceleration mechanisms including the self-consistent quasilinear theory. Some remarks on super-diffusion are included, stressing that super-diffusion takes place only at times shorter than binary collision time. Substantial space is provided for the discussion of particle injection based on observation and numerical simulation. Electron acceleration at shocks fills a long subsection. The nonlinear generation of high-energy tails on the electron distribution is discussed referring to shock particle simulations.

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Notes

  1. 1.

    We do not treat relativistic shocks in the present treatise. Inclusion of relativistic effects changes the structure of shocks substantially as also the acceleration of particles. Relativistic flows are already high speed with velocity close to c, thus acceleration implies gain in momentum and energy, and readily leads to particle creation and other effects which do not allow to separate anymore between fields and particles.

References

  • Amano T, Hoshino M (2007) Electron injection at high Mach number quasi-perpendicular shocks: surfing and drift acceleration. Astrophys J 661:190–202. doi:10.1086/513599

    ADS  Google Scholar 

  • Amano T, Hoshino M (2009a) Electron shock surfing acceleration in multidimensions: two-dimensional particle-in-cell simulation of collisionless perpendicular shock. Astrophys J 690:244–251. doi:10.1088/0004-637X/690/1/244

    ADS  Google Scholar 

  • Amano T, Hoshino M (2009) Nonlinear evolution of Buneman instability and its implication for electron acceleration in high Mach number collisionless perpendicular shocks. Phys Plasmas 16:102901. doi:10.1063/1.3240336

    ADS  Google Scholar 

  • Amano T, Hoshino M (2010) A critical Mach number for electron injection in collisionless shocks. Phys Rev Lett 104:181102. doi:10.1103/PhysRevLett.104.181102

    ADS  Google Scholar 

  • Asbridge JR, Bame SJ, Strong IB (1968) Outward flow of protons from the Earth’s bow shock. J Geophys Res 73:5777–5782. doi:10.1029/JA073i017p05777

    ADS  Google Scholar 

  • Axford WI, Leer E, Skadron G (1977) Acceleration of cosmic rays at shock waves. In: Proc XVth int conf cosmic rays, vol 11, pp 132–137

    Google Scholar 

  • Bale SD, Hull A, Larson DE, Lin RP, Muschietti L, Kellogg PJ, Goetz K, Monson SJ (2002) Electrostatic turbulence and Debye-scale structures associated with electron thermalization at collisionless shocks. Astrophys J 575:L25–L28. doi:10.1086/342609

    ADS  Google Scholar 

  • Bale SD, Kellogg PJ, Larson DE, Lin RP, Goetz K, Lepping RP (1998) Bipolar electrostatic structures in the shock transition region: evidence of electron phase space holes. Geophys Res Lett 25:2929–2932. doi:10.1029/98GL02111

    ADS  Google Scholar 

  • Bale SD, Mozer FS (2007) Measurement of large parallel and perpendicular electric fields on electron spatial scales in the terrestrial bow shock. Phys Rev Lett 98:205001. doi:10.1103/PhysRevLett.98.205001

    ADS  Google Scholar 

  • Balogh A, Erdös G (1983) Bidirectional distribution of energetic protons in the 18 February 1979 interplanetary shock event. Planet Space Sci 31:1389–1395. doi:10.1016/0032-0633(83)90014-4

    ADS  Google Scholar 

  • Balogh A, Erdös G (1985) Pitch angle distributions of 35–1000 keV protons at quasi-perpendicular interplanetary shocks. In: 19th int cosmic ray conf, vol 4, pp 178–181. (SEE N85-34729 23-92)

    Google Scholar 

  • Balogh A, Erdös G (1991) Fast acceleration of ions at quasi-perpendicular shocks. J Geophys Res 96:15853–15862. doi:10.1029/91JA01261

    ADS  Google Scholar 

  • Behlke R, André M, Bale SD, Pickett JS, Cattell CA, Lucek EA, Balogh A (2004) Solitary structures associated with short large-amplitude magnetic structures (SLAMS) upstream of the Earth’s quasi-parallel bow shock. Geophys Res Lett 31:L16805. doi:10.1029/2004GL019524

    ADS  Google Scholar 

  • Bell AR (1978) The acceleration of cosmic rays in shock fronts. Mon Not R Astron Soc 182:147–156. 443-455

    ADS  Google Scholar 

  • Biskamp D (2003) Magnetohydrodynamic turbulence. Cambridge Univ. Press, Cambridge, p 297

    MATH  Google Scholar 

  • Blandford R, Eichler D (1987) Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys Rep 154:1–75. doi:10.1016/0370-1573(87)90134-7

    ADS  Google Scholar 

  • Burgess D (1987) Shock drift acceleration at low energies. J Geophys Res 92:1119–1130. doi:10.1029/JA092iA02p01119

    ADS  Google Scholar 

  • Bykov AM, Treumann RA (2011) Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks. Astron Astrophys Rev 19:42. doi:10.1007/s00159-011-0042-8

    ADS  Google Scholar 

  • Cronin J, Gaisser TK, Swordy SP (1997) Cosmic rays at the energy frontier. Sci Am 276:32–37

    ADS  Google Scholar 

  • Davis L Jr (1956) Modified Fermi mechanism for the acceleration of cosmic rays. Phys Rev 101:351–358. doi:10.1103/PhysRev.101.351

    ADS  Google Scholar 

  • Drury LO’C (1983) An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep Prog Phys 46:973–1027. doi:10.1088/0034-4885/46/8/002

    ADS  Google Scholar 

  • Edmiston JP, Kennel CF, Eichler D (1982) Escape of heated ions upstream of quasi-parallel shocks. Geophys Res Lett 9:531–534. doi:10.1029/GL009i005p00531

    ADS  Google Scholar 

  • Eichler D (1981a) A cosmic-ray-mediated shock in the solar system. Astrophys J 247:1089–1092. doi:10.1086/15911

    ADS  Google Scholar 

  • Eichler D (1981b) Energetic particle spectra in finite shocks – the Earth’s bow shock. Astrophys J 244:711–716. doi:10.1086/158748

    ADS  Google Scholar 

  • Ellison DC, Möbius E, Paschmann G (1990) Particle injection and acceleration at Earth’s bow shock – comparison of upstream and downstream events. Astrophys J 352:376–394. doi:10.1086/168544

    ADS  Google Scholar 

  • Erdös G, Balogh A (1990) The acceleration of low energy protons by quasi-perpendicular interplanetary shocks. Planet Space Sci 38:343–353. doi:10.1016/0032-0633(90)90100-5

    ADS  Google Scholar 

  • Erdös G, Balogh A (1994) Drift acceleration at interplanetary shocks. Astrophys J Suppl 90:553–559. doi:10.1086/191874

    ADS  Google Scholar 

  • Fermi E (1949) On the origin of the cosmic radiation. Phys Rev 75:1169–1174. doi:10.1103/PhysRev.75.1169

    ADS  MATH  Google Scholar 

  • Forman MA, Webb GM (1985) Acceleration of energetic particles. In: Stone RG, Tsurutani BT (eds) Collisionless shocks in the heliosphere: a tutorial review. AGU, Washington, pp 91–114

    Google Scholar 

  • Fuselier SA (1995) Ion distributions in the Earth’s foreshock upstream from the bow shock. Adv Space Res 15:43–52. doi:10.1016/0273-1177(94)00083-D

    ADS  Google Scholar 

  • Giacalone J (2003) The physics of particle acceleration by collisionless shocks. Planet Space Sci 51:659–664. doi:10.1016/S0032-0633(03)00101-6

    ADS  Google Scholar 

  • Giacalone J (2004) Large-scale hybrid simulations of particle acceleration at a parallel shock. Astrophys J 609:452–458. doi:10.1086/421043

    ADS  Google Scholar 

  • Giacalone J (2005a) Particle acceleration at shocks moving through an irregular magnetic field. Astrophys J 624:765–772. doi:10.1086/429265

    ADS  Google Scholar 

  • Giacalone J (2005b) The efficient acceleration of thermal protons by perpendicular shocks. Astrophys J 628:L37–L40. doi:10.1086/432510

    ADS  Google Scholar 

  • Giacalone J, Jokipii JR (1999) The transport of cosmic rays across a turbulent magnetic field. Astrophys J 520:204–214. doi:10.1086/307452

    ADS  Google Scholar 

  • Giacalone J, Neugebauer M (2008) The energy spectrum of energetic particles downstream of turbulent collisionless shocks. Astrophys J 673:629–636. doi:10.1086/524008

    ADS  Google Scholar 

  • Goldstein ML, Roberts DA, Matthaeus WM (1995) Magnetohydrodynamic turbulence in the solar wind. Annu Rev Astron Astrophys 33:283–325. doi:10.1146/annurev.aa.33.090195.001435

    ADS  Google Scholar 

  • Goodrich CC, Scudder JD (1984) The adiabatic energy change of plasma electrons and the frame dependence of the cross-shock potential at collisionless magnetosonic shock waves. J Geophys Res 89:6654–6662. doi:10.1029/JA089iA08p06654

    ADS  Google Scholar 

  • Hamza AM, Meziane K (2011) On turbulence in the quasi-perpendicular bow shock. Planet Space Sci 59:475–481. doi:10.1016/j.pss.2010.03.013

    ADS  Google Scholar 

  • Hoppe M, Russell CT, Frank LA, Eastman TE, Greenstadt EW (1981) Upstream hydromagnetic waves and their association with backstreaming ion populations – ISEE 1 and 2 observations. J Geophys Res 86:4471–4492. doi:10.1029/JA086iA06p04471

    ADS  Google Scholar 

  • Hoshino M (2001) Nonthermal particle acceleration in shock front region: “shock surfing accelerations”. Prog Theor Phys Suppl 143:149–181. doi:10.1143/PTPS.143.149

    ADS  Google Scholar 

  • Hoshino M, Shimada N (2002) Nonthermal electrons at high Mach number shocks: electron shock surfing acceleration. Astrophys J 572:880–887. doi:10.1086/340454

    ADS  Google Scholar 

  • Hull AJ, Larson DE, Wilber M, Scudder JD, Mozer FS, Russell CT, Bale SD (2006) Large-amplitude electrostatic waves associated with magnetic ramp substructure at Earth’s bow shock. Geophys Res Lett 33:L15104. doi:10.1029/2005GL025564

    ADS  Google Scholar 

  • Ipavich FM, Galvin AB, Gloeckler G, Scholer M, Hovestadt D (1981a) A statistical survey of ions observed upstream of the Earth’s bow shock – energy spectra, composition, and spatial variation. J Geophys Res 86:4337–4342. doi:10.1029/JA086iA06p04337

    ADS  Google Scholar 

  • Ipavich FM, Gloeckler G, Scholer M (1981b) Temporal development of composition, spectra, and anisotropies during upstream particle events. J Geophys Res 86:1153–1160. doi:10.1029/JA086iA13p11153

    Google Scholar 

  • Jokipii JR (1966) Pitch-angle dependence of first-order Fermi acceleration at shock fronts. Astrophys J 145:616–622. doi:10.1086/148800

    ADS  Google Scholar 

  • Jokipii JR (1971) Propagation of cosmic rays in the solar wind. Rev Geophys 9:27–87. doi:10.1029/RG009i001p00027

    ADS  Google Scholar 

  • Jones FC (1990) The generalized diffusion-convection equation. Astrophys J 361:162–172. doi:10.1086/169179

    ADS  Google Scholar 

  • Jones FC, Ellison DC (1991) The plasma physics of shock acceleration. Space Sci Rev 58:259–346. doi:10.1007/BF01206003

    ADS  Google Scholar 

  • Kis A, Scholer M, Klecker B, Möbius E, Lucek EA, Rème H, Bosqued JM, Kistler LM, Kucharek H (2004) Multi-spacecraft observations of diffuse ions upstream of Earth’s bow shock. Geophys Res Lett 31:L20801. doi:10.1029/2004GL020759

    ADS  Google Scholar 

  • Kucharek H, Scholer M (1991) Origin of diffuse superthermal ions at quasi-parallel supercritical collisionless shocks. J Geophys Res 96:21195–21205. doi:10.1029/91JA02321

    ADS  Google Scholar 

  • Lee MA (1982) Coupled hydromagnetic wave excitation and ion acceleration upstream of the Earth’s bow shock. J Geophys Res 87:5063–5080. doi:10.1029/JA087iA07p05063

    ADS  Google Scholar 

  • Lévy P (1954) Théorie de l’addition des variables Aléatoires. Gauthier-Villars, Paris

    MATH  Google Scholar 

  • Lin RP, Meng CI, Anderson KA (1974) 30- to 100-keV protons upstream from the Earth’s bow shock. J Geophys Res 79:489–498. doi:10.1029/JA079i004p00489

    ADS  Google Scholar 

  • Mandt ME, Kan JR (1985) Effects of electron pressure in quasi-parallel collisionless shocks. J Geophys Res 90:115–121. doi:10.1029/JA090iA01p00115

    ADS  Google Scholar 

  • Matsukiyo S, Scholer M (2003) Modified two-stream instability in the foot of high Mach number quasi-perpendicular shocks. J Geophys Res 108:1459. doi:10.1029/2003JA010080

    Google Scholar 

  • Matsukiyo S, Scholer M (2006) On microinstabilities in the foot of high Mach number perpendicular shocks. J Geophys Res 111:A06104. doi:10.1029/2005JA011409

    Google Scholar 

  • Matsumoto H et al (1997) Plasma waves in the upstream and bow shock regions observed by geotail. Adv Space Res 20:683–693. doi:10.1016/S0273-1177(97)00456-0

    ADS  Google Scholar 

  • Matthaeus WH, Qin G, Bieber JW, Zank GP (2003) Nonlinear collisionless perpendicular diffusion of charged particles. Astrophys J 590:L53–L56. doi:10.1086/376613

    ADS  Google Scholar 

  • Metzler R, Klafter J (2000) The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 339:1–77. doi:10.1016/S0370-1573(00)00070-3

    MathSciNet  ADS  MATH  Google Scholar 

  • Miller JA (1991) Magnetohydrodynamic turbulence dissipation and stochastic proton acceleration in solar flares. Astrophys J 376:342–354. doi:10.1086/170284

    ADS  Google Scholar 

  • Miller JA, Guessoum N, Ramaty R (1990) Stochastic Fermi acceleration in solar flares. Astrophys J 361:701–708. doi:10.1086/169233

    ADS  Google Scholar 

  • Narita Y, Glassmeier K, Schäfer S, Motschmann U, Fränz M, Dondouras I, Fornacon K, Georgescu E, Koprth A, Rème H, Richter I (2004) Alfvén waves in the foreshock propagating upstream in the plasma rest frame: statistics from Cluster observations. Ann Geophys 22:2315–2323. doi:10.5194/angeo-22-2315-2004

    ADS  Google Scholar 

  • Narita Y, Glassmeier KH, Fornacon KH, Richter I, Schäfer S, Motschmann U, Dandouras I, Rème H, Georgescu E (2006) Low-frequency wave characteristics in the upstream and downstream regime of the terrestrial bow shock. J Geophys Res 111:A01203. doi:10.1029/2005JA011231

    Google Scholar 

  • Narita Y, Glassmeier K-H, Goldstein ML, Treumann RA, Gary SP (2008) Wave number spectra in the solar wind as seen by CLUSTER spacecraft. In: AGU Fall Meeting 2007, Abstract SH32B-07

    Google Scholar 

  • Narita Y, Glassmeier K-H, Treumann RA (2006) Wave-number spectra and intermittency in the terrestrial foreshock region. Phys Rev Lett 97:191101. doi:10.1103/PhysRevLett.97.191101

    ADS  Google Scholar 

  • Ohsawa Y (1985a) Strong ion acceleration by a collisionless magnetosonic shock wave propagating perpendicularly to a magnetic field. Phys Fluids 28:2130–2136. doi:10.1063/1.865394

    ADS  Google Scholar 

  • Ohsawa Y (1985b) Resonant ion acceleration by collisionless magnetosonic shock wave propagating obliquely to a magnetic field. J Phys Soc Jpn 54:4073–4076. doi:10.1143/JPSJ.54.1657

    ADS  Google Scholar 

  • Oka M, Terasawa T, Seki Y, Fujimoto M, Kasaba Y, Kojima H, Shinohara I, Matsui H, Matsumoto H, Saito Y, Mukai T (2006) Whistler critical Mach number and electron acceleration at the bow shock: geotail observation. Geophys Res Lett 33:L24104. doi:10.1029/2006GL028156

    ADS  Google Scholar 

  • Parker EN (1965) The passage of energetic charged particles through interplanetary space. Planet Space Sci 13:9–49. doi:10.1016/0032-0633(65)90131-5

    ADS  Google Scholar 

  • Reames DV (1999) Particle acceleration at the Sun and in the heliosphere. Space Sci Rev 90:413–491. doi:10.1023/A:1005105831781

    ADS  Google Scholar 

  • Rechester AB, Rosenbluth MR (1978) Electron heat transport in a Tokamak with destroyed magnetic surfaces. Phys Rev Lett 40:38–41. doi:10.1103/PhysRevLett.40.38

    ADS  Google Scholar 

  • Sagdeev RZ (1966) Cooperative phenomena and shock waves in collisionless plasmas. In: Leontovich MA (ed) Rev plasma phys, vol 4. Consultants Bureau, New York, pp 23–91

    Google Scholar 

  • Sagdeev RZ, Shapiro VD (1973) Influence of transverse magnetic field on Landau damping. JETP Lett Engl Transl 17:279–283

    ADS  Google Scholar 

  • Schlickeiser R (2002) Cosmic ray astrophysics. Springer, Berlin, p 519

    Google Scholar 

  • Scholer M (1985) Diffusive acceleration. In: Tsurutani BT, Stone RG (eds) Collisionless shocks in the heliosphere: reviews of current research. AGU, Washington, pp 287–301

    Google Scholar 

  • Scholer M (1990) Diffuse ions at a quasi-parallel collisionless shock – simulations. Geophys Res Lett 17:1821–1824. doi:10.1029/GL017i011p01821

    ADS  Google Scholar 

  • Scholer M, Kucharek H (1999) Interaction of pickup ions with quasi-parallel shocks. Geophys Res Lett 26:29–32. doi:10.1029/1998GL900239

    ADS  Google Scholar 

  • Scholer M, Kucharek H, Giacalone J (2000) Cross-field diffusion of charged particles and the problem of ion injection and acceleration at quasi-perpendicular shocks. J Geophys Res 105:18285–18293. doi:10.1029/1999JA000324

    ADS  Google Scholar 

  • Scholer M, Kucharek H, Kato C (2002) On ion injection at quasiparallel shocks. Phys Plasmas 10:4293–4300. doi:10.1063/1.1508441

    ADS  Google Scholar 

  • Scholer M, Kucharek H, Trattner K-H (1998) Injection and acceleration of energetic particles at collisionless shocks. Adv Space Res 21:533–542. doi:10.1016/S0273-1177(97)00958-7

    ADS  Google Scholar 

  • Scholer M, Kucharek H, Trattner K-H (1999) Injection and acceleration of H+ and He2+ at Earth’s bow shock. Ann Geophys 17:583–594. doi:10.1007/s00585-999-0583-6

    ADS  Google Scholar 

  • Scholer M, Trattner K-H, Kucharek H (1992) Ion injection and Fermi acceleration at Earth’s bow shock – the 1984 September 12 event revisited. Astrophys J 395:657–681. doi:10.1086/171687

    Google Scholar 

  • Scudder JD, Burlaga LF, Greenstadt EW (1984) Scale lengths in quasi-parallel shocks. J Geophys Res 89:7545–7550. doi:10.1029/JA089iA09p07545

    ADS  MATH  Google Scholar 

  • Sckopke N, Paschmann G, Bame SJ, Gosling JT, Russell CT (1983) Evolution of ion distributions across the nearly perpendicular bow shock – specularly and non-specularly reflected-gyrating ions. J Geophys Res 88:6121–6136. doi:10.1029/JA088iA08p06121

    ADS  Google Scholar 

  • Shlesinger MF, Zaslavsky GM, Klafter J (1993) Strange kinetics. Nature 363:31–37. doi:10.1038/363031a0

    ADS  Google Scholar 

  • Sonnerup BUÖ (1969) Acceleration of particles reflected at a shock front. J Geophys Res 74:1301–1304. doi:10.1029/JA074i005p01301

    ADS  Google Scholar 

  • Sugiyama T, Fujimoto M, Mukai T (2001) Quick ion injection and acceleration at quasi-parallel shocks. J Geophys Res 106:21657–21673. doi:10.1029/2001JA900063

    ADS  Google Scholar 

  • Sugiyama T, Terasawa T (1999) A scatter-free ion acceleration process in the parallel shock. Adv Space Res 24:73–77. doi:10.1016/S0273-1177(99)00427-5

    ADS  Google Scholar 

  • Tanaka M, Goodrich CC, Winske D, Papadopoulos K (1983) A source of the backstreaming ion beams in the foreshock region. J Geophys Res 88:3046–3054. doi:10.1029/JA088iA04p03046

    ADS  Google Scholar 

  • Terasawa T, Scholer M, Ipavich FM (1985) Anisotropy observation of diffuse ions (greater than 30 keV/e) upstream of the Earth’s bow shock. J Geophys Res 90:249–260. doi:10.1029/JA090iA01p00249

    ADS  Google Scholar 

  • Trattner KJ, Mobius E, Scholer M, Klecker B, Hilchenbachc M, Luehr H (1994) Statistical analysis of diffuse ion events upstream of the Earth’s bow shock. J Geophys Res 99:13389–13400. doi:10.1029/94JA00576

    ADS  Google Scholar 

  • Trattner KJ, Scholer M (1994) Diffuse minor ions upstream of simulated quasi-parallel shocks. J Geophys Res 99:6637–6650. doi:10.1029/93JA03165

    ADS  Google Scholar 

  • Treumann RA (1997) Theory of super-diffusion for the magnetopause. Geophys Res Lett 24:1727–1730. doi:10.1029/97GL01760

    ADS  Google Scholar 

  • Treumann RA (1999a) Kinetic theoretical foundation of Lorentzian statistical mechanics. Phys Scr 59:19–26. doi:10.1238/Physica.Regular.059a00019

    MathSciNet  ADS  MATH  Google Scholar 

  • Treumann RA (1999b) Generalized-Lorentzian thermodynamics. Phys Scr 59:204–214. doi:10.1238/Physica.Regular.059a00204

    MathSciNet  ADS  MATH  Google Scholar 

  • Treumann RA, Jaroschek CH (2008) Gibbsian theory of power-law distributions. Phys Rev Lett 100:155005. doi:10.1193/PhysRevLett.100.155005

    ADS  Google Scholar 

  • Tu C-Y, Marsch E (1995) MHD structures, waves and turbulence in the solar wind: observations and theories. Space Sci Rev 73:1–210. doi:10.1007/BF00748891

    ADS  Google Scholar 

  • Waxman E (2006) Gamma-ray bursts and collisionless shocks. Plasma Phys Control Fusion 48:B137–B151. doi:10.1088/0741-3335/48/12B/S14

    Google Scholar 

  • Wu CS (1984) A fast Fermi process – energetic electrons accelerated by a nearly perpendicular bow shock. J Geophys Res 89:8857–8862. doi:10.1029/JA089iA10p08857

    ADS  Google Scholar 

  • Yoon PH (2012a) Electron kappa distribution and steady-state Langmuir turbulence. Phys Plasmas 19:052301. doi:10.1063/1.4710515

    ADS  Google Scholar 

  • Yoon PH (2012b) Asymptotic equilibrium between Langmuir turbulence and suprathermal electrons in three dimensions. Phys Plasmas 19:012304. doi:10.1063/1.3676159

    ADS  Google Scholar 

  • Yoon PH, Ziebell LF, Gaelzer R, Lin RP, Wang L (2012) Langmuir turbulence and suprathermal electrons. Space Sci Rev 173:459–489. doi:10.1007/s11214-012-9867-3

    ADS  Google Scholar 

  • Zank GP, Li G, Florinski V, Matthaeus WH, Webb GM, le Roux JA (2004) Perpendicular diffusion coefficient for charged particles of arbitrary energy. J Geophys Res 109:A04107. doi:10.1029/2003JA010301

    Google Scholar 

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Authors and Affiliations

  1. The Blackett Laboratory, Imperial College London, London, UK

    Prof. Dr. André Balogh

  2. International Space Science Institute ISSI, Bern, Switzerland

    Prof. Dr. André Balogh & Prof. Dr. Rudolf A. Treumann

  3. Department of Geophysicsand Environmental Sciences, Munich University, Munich, Germany

    Prof. Dr. Rudolf A. Treumann

  4. Dartmouth College, Hanover, NH, USA

    Prof. Dr. Rudolf A. Treumann

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Balogh, A., Treumann, R.A. (2013). Particle Acceleration. In: Physics of Collisionless Shocks. ISSI Scientific Report Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6099-2_7

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