Bindu, S

Renuka, G

Sindhu, M S

Venugopal, C

IACS Institutional Repository

Indian J. Phys. 6 8 B (5), 443-449 (1994)U P  B- an international journalPlasma ^-parameter, plasma sheet wave temperature and AE indexS Bindu\ G Renuka \  M S Sindhu  ^and C Venugopal^* Department o f  Physics, University o f  Kerala, Kariavattom, Tnvandrum-695 581. India ^School o f  Pure and Applied Physics. Mahatma Gandhi University, Kottayam-686 562, IndiaReceived 3 March 1994, accepted 26 July 1994A b stra c t : The wave temperature o f  ULF Alfv^n wave propagating in the z-direction o f  the resonance layer o f  the plasma sheet is computed for twenty-two isolated substorms and their variation with plasma p  at the substorm onset are studied. The energy dissipation rates in the resonance layer in terms o f  and magnetic flux <P are computed and the dependence with p  are verified. The maximum energy dissipation rate when the plasma sheet temperature equals the wave temperature are computed and the dependence with plasma p  is found as linear. The thermal energy developed in the resonance layer due to the propagation o f  the wave is computed for 22 substorm  events and their correlation with AE index and p  are made.K e y w o r d s  : Plasma p, wave temperature, AE indexP A C S  N o. 52 .35 .P y1. IntroductionThe studies on the non-adiabatic motion of charged particles in the plasma sheet of the geomagnetotail has been fully appreciated only recently. The auroral electrojet index AE correlates well with the temperature on the plasma sheet [1]. During geomagnetic activity, the thermal energy in the plasma sheet increases [2]. Obviously detailed information on plasma p, which indicates the relative importance of thermal energy density of particles as compared to magnetic field energy density at substorm onset, provide insight into substorm physics. In order to obtain a further understanding of the behaviour of the geotail plasma sheet during substorms, we need more detailed information on plasma jS, energy dissipation rate in the plasma sheet and Alfv^n wave temperature [3].The plasma sheet parameters including plasma p  at substorm onset derived from GEOS 2 observations have been derived [4]. The expression for the wave temperature forO 1994 lACS444 S Bindu, G Renuka, M  S Sindhu and C VenugopalULF wave propagating in the z-direction with an Alfven speed in the plasma sheet have been derived f5]. They also derived expression for the energy dissipation rate integrated over the resonance layer of the plasma sheet. The expression for the energy dissipation rate during magnetospheric substorms were given by [6], The magnetic flux <P, the power transferred P and the energy developed E in the plasma sheet during substroms during the solar cycle 1965-1986 were computed recently [7].The purpose of this work is to investigate the nature of ULF wave temperature propagating in the z-direction through the resonance layer of the plasma sheet at substorm onsets and also its variation with plasma p. The dependence of the energy dissipation rates in the resonance layer in terms of wave temperature and magnetic flux 0  are investigated. The relationship between AE index, thermal energy E„ and plasma P are studied. The values of the energy dissipation rate when T = T^ , are also computed.2. Chaotic motion of a protonConsider the perturbation displacement of a proton in the z-direction along a closed field line with antisunward propagating ULF waves with wave vector k = k^ ,^  6) and frequency o).These ULF waves, perturb a field line with a parallel wave number k and excite oscillations of this field line at its own resonance frequency If cu= oscillations will grow to a very high amplitude and a resonance layer develops between the lobe and neutral sheet.The energy dissipation rate Q integrated over the resonance layer and the wave temperature are given by [5]andQ = An^AzP/^^  [(r/T-^ -  i f  + n'^k'^Az^ T ^ .  -  1 / 2 m, c o ^ / k l  { k j k ) ! \  +  2 / p ,(1)(2)where Az 'is the scale length of the gradient of the Alfven speed in the resonance layer where the absorption of ULF waves occur. P is the power of the wave with frequency /  and amplitude z and is related to the amplitude of the magnetic fluctuations in the lobe (-  1(H -  10' ,^ nT^-Hz) [8], T is the temperature on the plasma sheet side of the resonance layer, n\ is the mass of the propagating ion. The energy dissipation rate in the magnetotail plasma sheet is given by [6]Q' = I V ^ R . (3)where 0  = B/2 n  Rj V JL  is the magnetic flux in the plasma sheet at substorm onset, L is the length of the plasma sheet, R j  is its thickness and is the solar wind speed.3. DataThe plasma p, B and R j  values of twenty-two isolated substorm events (designated as storm 1-22) derived from GEOS 2 observations at plasma sheet are collected [4]. The wave number of the propagating ULF wave at Alfv6n velocity is calculated. P is taken asPlasma ^-parameter, plasma sheet wave temperature and AE index 4450.015 nT^—Hz. The AE indices for the 22 events are collected from the Data Book supplied by WDC C2 for Geomagnetism.4. Results and discussionsUsing eqs. (1). (2) and (3), the wave temperature Ty, of the propagating ULF wave, the energy dissipation rates Q and Q' are computed. The thermal energy E„ in the resonance layer at the substorm onsets and the energy dissipation rates in the resonance layer when the temperature of the plasma sheet T equals the wave temperature for the twenty-two isolated substorms are also calculated.Table 1 shows the correlation between the magnetic field strength in the resonance layer at substorm onset, the thermal energy AE index and the plasma /?. From Table 1, itT ab le  1. Substorm events and plasma sheet parameters.Storm AE BnT keVAug. 03, Oct. 17, N ov 11, N ov. 21, N ov. 26, D ec. 04, Jan. 22, Jan. 25, Jan. 26, Jan. 27, Feb, 06, Feb. 18. Feb. 26, Mar. 04, Mar. 24, Mar. 25, May 23, May 27, June 20, July 03, July 16, July 27,1978197819781978197819781979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 1979 197926978199202382160217379410281300273431314226439267426213229225248614870827753 86 69 697576  84 76  9054  60  63 69  69  56  62  1133.9 2.2 1 6 0.93.03.12.1 2.14.9  3 53.9 2.01.9 1.0 2.6 2.8 1.01 0^ 1.8 0.8 1.3 4.21 738 0 607 0 9.39 0.7252 131 1.042 1.860 1.197 2 793 2.357  2.697 1.690 1.314 0.970  0.907  1.207 0.475  0.570  1.026 3.004  0.598  6.442is clear that the maximum value of is obtained corresponding to /? of 4.2 and AE index 248. The minimum value ofE„ corresponds to ^ of 1.0 and AE index 267. The values of446 S Bindu, G Renuka, M  S Sindhu and C Venugopalcorresponding to maximum and minimum values of /? are respectively 2.793 keV and 3.004 keV.Figure 1 is the graphical representation of the variation of the wave temperature of ULF Alfvdn wave during the 22 substorm events. From y3-values of the corresponding storms, it is found that as jS increases, the wave temperature increases and at a particulai value'o*Kto |37343.1 262.52.21.91.6 1.3 1.0 ,Figure 1. Variation o f  wave temperature with ^  during 22 substorm events.of p, the wave temperature begins to decrease. We have obtained a peak value of as 3.492 keV corresponding to /J of 2.1 (storm 8). The minimum value of Ty^  obtained is 1.070 keV corresponding to maximum P = 4.9 (storm 9). Hence for maximum value of )3, is minimum and the resonance layer heating is minimum. The resonance layer shows a slight variation of 7^ between storm 15 and 22. As the heating rate is never zero, the wave acquires a maximum temperature when the plasma sheet heating is balanced by the loss through convection or through heat conduction into the-ionosphere [5]. This convection of plasma is through the resonance layer. In thermal catastrophe model of substorm triggered plasma sheet, temperature is correlated positively with AE index and suggests that under the appropriate conditions, Alfv6n waves are absorbed in the resonance layer near the edge of the plasma sheet. This gives rise to an increase of thermal energy within the RL. The degree and duration of heating process in the resonance layer depend on the convection speeds within the PS. This model allows the resonance layer to extend in the x-direction and energization at several locations [9]. As p  further increases, the convection or conduction rate also increases and wave temperature decreases and thus plasma sheet heating decreases. So the plasma p  plays an important role in thermal catastrophe.The variation of energy dissipation rates Q (curve a) and Q'  (curve b) over the resonance layer of the plasma sheet during 22 substorm events are shown in Figure 2. From curve a, it is found that as p  increases Q also increases, reaches a maximum and then begins to decrease.to decrease. The maximum value of Q obtained is 101.92 x lO* J/sec corresponding to p  of 2.1. Curve b also gives the same nature as curve a. Maximum Q'  obtained is 104.92 x 10® J/sec for a ^ of 2 .1. Theminimum valueof e 'is6 0 .8 4 x  10® J/sec fora ^ of 0.8 (storm 20)110»Plasma p-parameter, plasma sheet wave temperature and AE index 447tf—^ PLASMA PF igu re 2, Variation o f  Q and G ' with P during 22 substorm events.and minimum of Q also corresponds to a of 0.8. This result is in agreement with the analytically intractable form of the energy dissipation [ 10]. From Figure 2, it is found that the energy dissipation rate Q is slightly less than Q \  This can be interpreted as that the absorption of energy waves occurs in a discontinuous fashion along z-dircction at the resonance layer and in a continuous manner in the presence of gradients in the quantity[10]. Also the nature of absorption due to Alfven mode propagation has been discussed by [11]. This continuous absorption serves to increase the enthalpy flux in the resonance layer which in turn, reduces the rate of dissipation of energy flux. The energy dissipation rate in the plasma sheet is a major sink for substorm energy comparable with the ionosphere. The statistical studies of Huang e td  [12] reveal that the plasma temperature is correlated with geomagnetic activity level. So the energy dissipation depends on the temperature of the plasma sheet which in turn, depends on plasma (i parameter. The works of Huang etal [12] reveal that the energy dissipation rate-variation in the plasma sheet at the time of substorms, support for the reconnection at the magnetotail.When the temperature on the plasma sheet of the resonance layer T is equal to the temperature of the propagating Alfven wave the energy dissipation rate is maximum (Figure 3). When T = there is a continuous increase of Q with )8. When T < the heating rate in the resonance layer increases and when T > the heating rate decreases. At T s= the heating rate has the maximum value. This result agrees well with [5]. The maximum value of |2 obtained is 136 x 10^  J/sec corresponding to maximum p  of 4.9. Also Q has minimum value 64.84 x 10^  J/sec when P = 0.8, the minimum value. The entropy change in the resonance layer in terms of Q is given asAS = [2/3 ( S e y p v j  ,where S is the specific entropy of the resonance layer, is the velocity of proton in the z-direction. This entropy-change invokes the heating mechanism in the thermal catastrophe448 ^  Bindu, G Renuka, M  S Sindhu and C VenugopalFigure 3. Maximum energy dissipation rate variation (when T = T J  With during 22 substorm events.model of the substoim-triggered plasma sheet. Since g  is a function of plasma /J parameter, the entropy changes are in accordance with the variation of [i. This entropy-change is active in the plasma sheet which leads to the loss of plasma through the formation of a neutral line and ejection of plasmoids.5. ConclusionThe response of the plasma sheet resonance layer to the wave temperature of ULF Alfven wave and the energy dissipation rate are studied. It has been possible to correlate the energy dissipation rates at the time of substorms in terms of 7 ,^ and ^  and to understand the energy absorption rate in the resonance layer. The nature of wave temperature of ULF wave propagating through the re.sonance layer in accordance with plasma p  and when T = 7vv» maximum energy dissipation rate variation with P are also studied. The wave temperature- change and the energy dissipation rate-variation studies invoke the heating mechanism in the resonance layer and thermal catastrophe model of the substorm-triggered plasma sheet. The current work will also help to account for the entropy change and to understand why chaos would occur in the resonance layer of the plasma sheet.AcknowledgmentThe authors would like to thank the referees for their valuable comments.Plasma p-parameter, plasma sheet wave temperature and A E index449R e fe r e n c e s[1] C Y Huang, C K Goertz, L A Frank and G Rostoker Geophys Re^ Lett 16 563 (1989)[2] C Y Huang and L A Frank Geophys. Res. Lett 13 652 (1986)[3J C K Goertz and R A Smith J. Geophys. Res. 94 6581 (1989)f4] Z Y Pu. A Korth and G KremserJ. Geophys. Res 97 19. 341 (1992)[5] C K Goertz. R A Smith and Lin-Hua Shan Geophys Re. .^ Lett 18 1639 (1991)[6] W D Gonzalez and F S Mozer J. Geophys. Res 79 4186 (1974)[7] S Bindu. G Renuka and C Venugopal Ann. Geophystcae (communicated) (1994)[8] C A Fitch and L-H Shan Geophys. Res Lett. 17 1845 (1990)[9] C K Goertz and R A Smith J. Geophys Res. 94 6581 (1989)[10] B G Harrold, C K Goertz. R A Smith and P J Hansen J. Geophys Re. .^ 95 15. 039 (1990)111] B H M aukandC  I Meng Phys. Scr. T 18  28 (1987)[12] C Y Huang. L A Frank, G Rostoker. J Fennell and D G Mitchell J  Geophys Res 97 1481 (1992)68B (5) 9

Plasma β-Parameter, Plasma Sheet Wave Temperature and AE Index

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Plasma β-Parameter, Plasma Sheet Wave Temperature and AE Index

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