Computer simulation of the nongyrotropic electron beam-plasma interaction

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1 Computer simulation of the nongrotropic electron eam-plasma interaction 1,3 Márcio A. E. de Moraes, 2 Yoshiharu Omura, 3 Maria V. Alves, 1 Universidade de Tauaté, Brail. 2 Koto Universit, Japan, 3 INPE, Brail Copright 2003, SBGf - Sociedade Brasileira de Geofísica This paper was prepared for presentation at the 8 th International Congress of The Brailian Geophsical Societ held in Rio de Janeiro, Brail, Septemer Contents of this paper were reviewed The Technical Committee of the 8 th International Congress of The Brailian Geophsical Societ and does not necessaril represents an position of the SBGf, its officers or memers. Electronic reproduction or storage of an part of this paper for commercial purposes without the written consent of The Brailian Geophsical Societ is prohiited. Astract In this paper we performed a computer simulation of the nongrotropic electron eam-plasma interaction ased on oservational data otained from ISEE 1 and 2. These data indicated the existence of nongrotropic electrons just upstream of the Earth s ow shock. In the simulation, the electron eam is assumed to have an extreme nongrotrop. We stud the possile electromagnetic emissions and clarif effects of the nongrotrop on nonlinear evolution of the electron eam instailities. In the nongrotropic case, we found that the magnetic field energ ecame much larger than in the grotropic case, indicating a strong electromagnetic wave emission. Introduction Distriution functions in magnetoplasmas of the tpe F( v, v ), where velocities occur oth parallel ( v ) and perpendicular ( v ) directions to the ackground magnetic field ( B r 0) are smmetric with respect to the magnetic field and are termed grotropic. When this smmetr is roken, the distriution ecomes grophase dependent or nongrotropic (Motschmann et al., 1997). Nongrotropic magnetoplasmas with a ackground magnetic field B r = Bx 0 0ˆ have at least one particle population whose unpertured distriution function depends on the grophase angle φ = arctg( v / v ) (Romeiras et al., 1999}. The effects of nongrotrop on linear wave dispersion were first studied in the context of fusion plasmas (Sudan, 1965; Eldridge et al., 1970). Several studies followed these pioneering researches. The showed that the introduction of grophase organiation (unching) can ring aout coupling among the parallel eingenmodes, with the associated free energ enhancing previousl existing (grotropic) instailities or, in otherwise stale media, generating wave growth (Romeiras et al., 1999; Brinca et al., 1992; Brinca et al., 1993; Brinca, 2000). Nongrotropic particle populations are frequentl encountered in space plasmas. Nongrotrop has een oserved in ion populations in the region at and just upstream of the Earth's ow shock (Thomsen et al., 1985), several Earth radii upstream (Gurgiolo et al.,1981) in the ion foreshock and downstream in the magnetosheath (Sckopke et al., 1990}. Measurements the ISEE 1 and ISEE 2 indicate the existence of nongrotropic electrons in these same regions (Anderson et al., 1985). In a recent work, a possile sustained signature of a non grotropic electron distriution just upstream of the Earth s ow shock was otained the ISTP WIND 3-D Plasma and Energetic Particle Experiment, showing several examples of electron nongrotrop (Gurgiolo et al., 2000). In this work we performed particle simulations of electron eam-plasma interaction in a one-dimensional sstem taken along the magnetic field. We introduced a nongrotrop in the particle population of an electron eam drifting against the ackground plasma. We stud possile electromagnetic emissions, and clarif effects of the nongrotrop on nonlinear evolution of electron eam instailities. In the nongrotropic case, we found that the magnetic field energ ecame much larger than in the grotropic case, indicating a strong electromagnetic wave emission Simulation Model We use a particle-in-cell code, KEMPO (Koto universit ElectroMagnetic Particle code) developed at Radio Atmospheric Science Center (Matsumoto and Omura, 1993) that allows spatial variations along the x -direction. Since we are interested aout parallel propagation, the wave vector of the modes is aligned with the x -direction, r k = kxˆ, with the amient magnetic field defined B r = Bx 0 0ˆ. Figure 1 shows the reference sstem used in our simulations Electron eam B 0 Figure 1 - Reference sstem used in our simulation. It shows an electron eam propagating parallel to the ackground magnetic field, oth in the x -direction of the sstem. x Eighth International Congress of The Brailian Geophsical Societ

2 Computer simulation nongrotropic electron eam For the proposed stud the simulation code incorporates three species of charged particles: ackground electron and ions, and an electron eam with a given drift velocit. We assume the ion species to e of infinite mass, providing a neutraliing ackground. Both eam and plasma electrons have Maxwelliana population. For grotropic (suscript G) and nongrotropic (suscript NG) cases the electrons of the eam are distriuted with a pitch angle α = 60, where α = arctg( v / v ) is the angle etween ackground magnetic field and the direction of motion of the particles. For the nongrotropic case the electron eam velocit component, v NG, is ero ( v NG = 0 ) and the v is assumed to have an additional value v0 16v the vng = vg + v0, introduced at t = 0. Velocit distriution functions of the moving particles, grotropic (top) and nongrotropic (ottom) cases, are shown in Figure 2, at t = 0. We can see the formation of a ring for the electron eam, in the grotropic case, and an extreme electron eam nongrotrop with grophase angle φ = 90, in the nongrotropic case. Boundar conditions are periodic and preexisting wave packets are not assumed, and all the waves grow self-consistentl out of noise. Electrostatic modes are investigated oserving the r r longitudinal wave electric fields ( E k xˆ ) whereas the electromagnetic modes oserving the wave field components ( E, E ), and ( B, B ). Parameters Values Electron plasma frequenc ( ω pe) 45.4 Ω Electron cclotron frequenc ( Ω e) 1.0 Ω electron thermal speed ( v the) c electron eam thermal speed ( v th) c electron eam drift velocit ( V d) 0.1c grid spacing ( x) 2.5λ D numer of grid points 4096 numer of superparticles time step Ω eam to plasma densit ratio ( n / n 0) Results and Discussion Simulation results presented in this section were otained using the parameters shown in Tale 1. Parameters were chosen ased on oservational data from measurements on ISEE 1 and ISEE 2 (Anderson et. al, 1985). The velocities are normalied with respect to v n, where vn = 2vth (suscript is related to the nongrotropic electron eam), and the frequencies are normalied with respect Ω. The resulting Dee length ( λd) is large enough (in the scale of the grid spacing) to avoid nonphsical heating of the plasma (Birdsal and Langdon, 1985). Figure 3 presents the time evolution of electrostatic and kinetic energ for the grotropic (left) and nongrotropic (right) case, oth in the logarithm scale for the axis. All the energies were normalied the initial magnetic 2 energ ( B 0 /2 µ 0). The nongrotropic case presents higher kinetic and electrostatic energies due to the introduction of v0 0 16vthe. We can oserve that oth cases present similar ehavior, the corresponding decreasing of kinetic energ appearing as an increasing of the electrostatic energ, in the eginning of simulation until t 2 Ω. After this time the kinetic energ ecame constant, in oth cases, and the electrostatic energ decreases slowl. Tale 1 Values of parameters used in the simulation. Figure 2 - Velocit distriution functions, at t = 0, for the grotropic (top) and nongrotropic (ottom) cases. Concerning the electromagnetic energ, we see that for the grotropic case there is no variation along the time, as Eighth International Congress of The Brailian Geophsical Societ

3 Computer simulation nongrotropic electron eam 3 shown in Figure 4 (left), just appearing fluctuations. For the nongrotropic case, we see an increasing of the electromagnetic energ as shown in Figure 4 (right). The growing of electromagnetic energ starts at t 4 Ω reaching the first maximum at t 10 Ω (the total time run simulation). This energ gain comes from the electrostatic energ that decreases along the simulation (see the Figure 3). The diagram ( ω k) tells us the modes that are present in the sstem. We constructed the ( ω k) diagram for the electromagnetic fields components ( Ex, E, E, B, B ). We will show the ( ω k) diagram for the E x, and E components. Figure 5 shows the ( ω k) diagram for E x component (electrostatic mode) for the grotropic (left) and the nongrotropic (right) cases, respectivel. Colors are related to the intensit of the field component (in db). For oth cases we oserve Langmuir waves, frequenc close to 45 Ω, forward and ackward propagating and also the eam mode forward propagating in the nongrotropic case. Figure 6 shows the ( ω k) diagram for the E component (electromagnetic mode) for the grotropic (left) and the nongrotropic (right) cases. For oth cases we oserve the RCP high frequenc mode, forward and ackward propagating. We also oserve the whistler mode (RCP low frequenc) in oth cases. For the nongrotropic case (right) the whistler mode emission is intensified. Colors are related to the intensit of the field component (in db). We also oserve in the nongrotropic case the presence of an electrostatic mode due the extreme electron nongrotrop, which ehaves like a eam mode. Figure 7 shows the distriution function of velocit, for the components, v and v for different times. This figure illustrates a rotating nongrotrop with frequenc Ω. Conclusions In this work we performed particle simulations of electron eam-plasma interaction in a one-dimensional sstem taken along the magnetic field. We introduced a nongrotrop in the particle population of an electron eam drifting against the ackground plasma. We compare the ehavior of two sstems, grotropic and nongrotropic. We oserve that at earl times, up to t 2 Ω, oth sstems have similar ehavior. For times larger than t 4 Ω, there is an enhancement of the electromagnetic energ for the nongrotropic case. An intensification of the emission of the whistler mode can e oserved in the ω k diagram for the E component (see Figure 6). Different grophase angles and densit eam to plasma ratios should e investigated in the near future Acknowledgments This work was supported FAPESP- Fundação Amparo à Pesquisa do Estado de São Paulo, and UNITAU Universidade de Tauaté, Brasil. References A. L. Brinca, J. Atmospheric and Solar-Terrestrial Phsics, 62, 701, A. L. Brinca, L. Borda de de Água, and D. Winske, Geophs. Res. Let. 12(24), 2445, A. L. Brinca, L. Borda de Água, and D. Winske, J. Geophs. Research, 98, 7549, C. Gurgiolo, G. K. Parks, B. H. Mauk, C. S. Lin, A. Anderson, R. P. Lin, and H. R, J. Geophs. Research, 86, 4415, C. k. Birdsall, and B. Langdon, Plasma Phsics via Computer Simulation, McGraw-Hill, NY, C. Gurgiolo, D. Larson, R. P. Lin and H. K. Wong, Geophsical Res. Lett., 27, 19, , F. J. Romeiras, and A. L. Brinca, J. Geophs. Res.104, 12407, K. A. Anderson, R. P. Lin, C. Gurgiolo, G. K. Parks, D. W. Potter, S. Werden, and H. R\UNICODE{0xe8}me, J. Geophs. Research, 90, 10809, M. F. Thomsen, J. T. Gosling, S. J. Bame, and C. T. Russel, J. Geophs. Research, 90, 267, Motschamann, U., Kafemann, H. and Scholer, M. A. Geophsicae, 15, 603, N. Sckopke, G. Paschmann, A. L. Brinca, C. W. Carlson, and H. L\UNICODE{0xfc}hr, J. Geophs. Research, 95, 6337, O. Eldridge, Phs. of Plasmas 13, 1791, R. N. Sudan, Phs. of Plasmas, 8, 1915, Y. Omura, and H. Matsumoto, in: Computer Space Plasma Phsics, ed. H. Matsumoto and Y. Omura, Chap.2, 21-84, Eighth International Congress of The Brailian Geophsical Societ

4 Computer simulation nongrotropic electron eam 4 Figure 3 - Time evolution of electrostatic and kinetic energ for the grotropic (left) and nongrotropic (right) cases. Figure 4 - Time evolution of electromagnetic energ for the grotropic (left) and nongrotropic (right) cases. Eighth International Congress of The Brailian Geophsical Societ

5 Computer simulation nongrotropic electron eam 5 Figure 5 - ω k diagram for the electric field component, E x, electrostatic, for the grotropic (left) and the nongrotropic (right) cases. Colors are related to the amplitude of the component. Figure 6 - ω k diagram for the electric field component, E, electrostatic, for the grotropic (left) and the nongrotropic (right) cases. Colors are related to the amplitude of the component. Eighth International Congress of The Brailian Geophsical Societ

6 Computer simulation nongrotropic electron eam 6 Figure 7 Contour plots of the distriution function, velocit components v and v, for the eam and plasma electrons for different time steps, in the nongrotropic case. Eighth International Congress of The Brailian Geophsical Societ