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Kinetic Processes in the Solar Wind William C. Feldman University of California, Los Alamos Scientific Laboratory Los Alamos, New Mexico 87545 767
768 1) Introduction The solar wind at 1 astronomical unit (AU) is a fully ionized plasma, consisting primarily of electrons, protons, and alpha particles, which streams away from the sun at supersonic speeds. It is a nearby and accessible example of a cosmic plasma. Studies of the internal physical state of the solar wind are of scientific interest in their own right as well ag for their relevance to several related physical and astrophysical disciplines. For example, such studies provide diagnostic information useful for placing constraints on theories of the coronal expansion. This information, is carried in part by the plasma ions and electrons and is evident in the characteristic shapes of particle velocity distributions at 1 All. It is also evident in the hydromagnetic wave field which consists primarily of large amplitude Alfve"n waves travelling away from the sun in the local solar wind rest frame, A second reason for interest in the solar wind is that it is convenient for studying the state and development of plasma turbulence in an astrophysical setting. The type and amplitude of the turbulence determines the rates at which processes such as magnetic field reconnection and particle acceleration proceed. It also regulates the efficiency with which the plasma conducts heat and transports linear and angular momentum. Studies of the kinetic state of the solar wind as it expands away from the sun are therefore of use in obtaining a quantitative understanding of the manner and rate at which a cosmic plasma evolves into a turbulent state as well as of the physics of turbulent processes postulated to be occurring in other astrophysical plasmas.
769 A third reason for studying the internal state of the solar wind is that the interplanetary medium near 1 AU provides a laboratory in which several (in general nonlinear) collisionless processes can be observed to occur. It is therefore possible to use solar wind observations to quantitatively test theories which hope to describe (and eventually allow a control over) the behaviour of laboratory fusion plasmas. In particular, they are of use for providing quantitative information concerning 1) the thresholds, nonlinear saturation mechanisms, and asymptotic wave levels of various plasma instabilities, 2) details of nonlinear Vlasov-Maxwell equilibria possible in collisionless plasmas, and 3) rates of energy and momentum transport within generally noisy, collisionless plasmas. Such information is essential for achieving the stable confinement of fusion plasmas in laboratory devices. For example, the physics of kinetic heat flux regulating mechanisms is only poorly understood, yet is very important for controlling end losses in magnetic confinement devices and for producing spherically symmetric pellet coronae while limiting the preheating of pellet targets in inertially confined devices. As will be detailed below, similar mechanisms may be active in the solar wind and are currently being explored both experimentally and theoretically. In addition, possible nonlinear equilibrium plasma configurations are largely unknown. However, a detailed knowledge of the various possible Vlasov-Maxwell equilibria is presently important to both laboratory and solar wind plasma research. Because of the large characteristic distances in inter- planetary space, the solar wind convects through a density scale height in about 10
770 proton gyro periods. As a result, there is generally more than enough time for it to reach a steady state with regard to its internal configuration. For comparison, a laboratory fusion device with a 50 kG magnetic field must confine a deuterium plasma for ahout 4 x 10 gyro periods if it is to operate stably for 1 msec; a minimum time estimated for economic operation. These periods are long compared to typical growth times of micro-instabilities driven by non-Maxwellian particle configurations which can possibly evolve because both the solar wind and laboratory fusion plasmas are at times collisionless. The interplanetary medium near 1 All therefore provides a laboratory for studying possible steady state configurations of a collisionless plasma. In contrast to the case in laboratory plasmas, very detailed, nonperturbing measurements are possible in the solar wind because at 1 All, the Debye length (10 m) is larger than an entire spacecraft. In this report we review some of the recent work on kinetic plasma processes active in the solar wind near 1 All. The scope of this review will be confined to processes with wavelengths shorter than about 10 proton gyroradii which are driven by non-Maxwellian particle velocity distributions. The very important and interesting problem of the origin of these distribu- tions is not considered. The reason for this decision is twofold. First, although many plausible explanations of the evolution of solar wind particle velocity distributions with distance from the sun have been given, and many more are possible, no plasma processes have been firmly established because of an absence of information about the internal state of the low and intermediate corona. Second a review of longer wavelength fluctuation phenomena of solar origin, which most likely strongly affects the internal state of the solar 14 wind near 1 AU, is covered in an accompanying report, A description of solar wind particle velocity distributions is given first in section 2. This description is followed in sections 3 through 5 by reviews of three of the
771 many different kinetic phenomena driven by non-equilibrium particle con- figurations which evolve in interplanetary space. In section 6 a brief description is given of a specific example of particle acceleration thought to occur in the solar wind near and beyond 1 All. Suggestions for future expansion of this research are given in section 7. Certain topics have been omitted because it would be premature to present them at their present stage of development. For example, the subjects of viscosity and angular momentum transport which are, at least in part, affected by processes considered in this review have not been included per se although they have important astrophysical application. In particular they are essential for understanding mechanisms 1) of angular momentum shedding in star formation, 2) of stellar spin down and 3) of interactions between binary stars which lead to substantial accretion and intense X-ray emission. Furthermore, although studies of interplanetary shocks and magnetic reconnection are of interest and have broad application, they are not reviewed here. Both subjects can be studied in far greater detail within 38 72 the near earth environment and are reviewed in companion reports. ' 2) Particle Velocity Distributions in the Solar Wind Near 1 AU a) Electrons During quiet conditions, interplanetary electrons of solar origin are observed over a broad range of energies spanning the interval 0 < E < 100 59 51 keV. ' ' In order to quantify the free energy carried by solar wind electrons it is convenient to subdivide the entire energy range into three distinct subranges. For typical quiet conditions the lowest subrange extends from zero to about 60 eV, the intermediate range extends from about 60 eV to several keV, and the highest range covers the interval between several keV up to about 100 keV.51'23
772 A cut through a typical solar wind electron velocity distribution along 24 59 58 the magnetic field direction, B, is shown in Fig. 1. The measured distribution, f , is plotted using solid dots and the lines represent two essentially bi-Maxwellian functions which fit the data best at low and intermediate electron energies respectively. The energy beyond which f rises above the bi-Maxwellian function, f , that characterizes f well at low energies, marks the boundary between the low and intermediate electron-energy subranges. Although for this example, the hotter bi-Maxwellian is seen to represent the measured velocity distribution, f = f - f , in the intermediate velocity range quite well, it is not a unique representation. A power law in energy, exponential in speed or some other analytic form may equally well describe f... At times, however, the bi-Maxwellian fits to f are definitely not acceptable. When the solar wind bulk speed is high, measured electron distributions are more strongly beamed (fu exhibits a large n thermal anisotropy) along the magnetic field direction than can be 25 accommodated by a single bi-Maxwellian function. In fact recent, more detailed measurements of solar wind electron velocity distributions, indicate a better characterization of fu in terms of a superposition of two separate rl components; a nearly isotropic hot component and a strongly beamed component " 57 travelling away from the sun but along B. Although this more complex characterization of fu is only required by two-dimensional measurements such n as shown in Fig. 1 in the high speed solar wind, it is more general and therefore probably more useful for understanding the development of the internal state of solar wind electrons during most flow conditions. Within the energy range spanning the interval between several keV and 100 keV during quiet conditions, interplanetary electron spectral intensities (electrons cm *~ s L sr keV ) follow a power law dependence, dj/dE a E with spectral index, 6â3.5. Although velocity distributions within this
773 energy range fit smoothly onto those measured at intermediate energies, the highest energy distributions are more isotropic. The above characterization of f allows a qualitative discussion of how measured electron velocity distributions deviate from simple bi-Maxwellian functions. A quantitative discussion using two of the many possible ways of 23 27 characterizing electron distributions is given elsewhere. i Under appropriate circumstances, these deviations can become sources of free energy leading to instability. The salient deviations are as follows. Electrons in the intermediate energy range are always hotter than those in the low energy range. Although with present two-dimensional measurements it appears possible to characterize the intermediate range electrons in the low speed solar wind in terms of single bi-Maxwellian, bi-Lorentzian, or other similarly shaped functions, this is not the case in the high speed solar wind. At high speeds, measured electron distributions are more complex and require a description consisting of at least two separate components as mentioned earlier. Furthermore, hot and cold electron components move A relative to one another along B in such a way that the net electron particle flux is zero in the frame of reference moving with the ions. In general, the hot component travels away from the sun faster than does the cold component. Although electrons in the highest energy range are generally distributed as a power law, occasionally a transient peak appears which moves from high to low energy with time (see e.g. Ref. 52). Peaks in the electron flux distributions near 1 AIT have been observed as high as 100 kev and as low as 39 ~6 keV, These secondary peaks are generally associated with interplanetary Type III
774 radio bursts and are thought to arise because of the tlansient nature of the source at the sun. ' ' A one-dimensional schematic illustration of this process is given in Fig. 2. For this purpose it is assumed that at time T , energy is deposited in a localized region near the base of the corona. The resultant electron heating produces an enhanced high energy extension on the coronal electron velocity distribution as shown in the top panel of the figure. At some location in interplanetary space a distance AR from the heating region, outwardly travelling electrons which were energized at time T , will be observed at time T in the velocity interval above some lower limit, V.. In the absence of significant scattering, velocity dispersion will therefore produce a peaked spectrum of heated electrons with a sharply cutoff lower velocity limit which depends on AR and T as V = AR/(T - T ). The total electron velocity distribution at AR will then consist of the sum of ambient low energy electrons and heated high energy electrons. A transient secondary electron peak should therefore appear at the speed V. (T ) which decreases monotonically with increasing time as illustrated in the lower three panels of Fig. 2. b) Protons Proton velocity distributions, f , measured in the solar wind near 1 AU range from isotropic Maxwellian to velocity resolved double streaming 21 configurations. Most of the time, and especially during high speed flow
775 conditions, f cannot be described by models consisting of simple extensions 7R 71 to a bi-Maxwellian shape which include a third velocity moment. ' " In fact a visual survey of measured proton distributions suggest that much of the time, they can be best described in terms of two unresolved, relatively drifting components, f = fM + f_. Here the subscripts M and B refer to main and beam proton components respectively. Such a description is demonstrated in Fig. 3 for two representative proton distributions measured 24 in the high speed solar wind. In the top two panels of Fig. 3, the squares give the measured velocity distribution integrated over velocities A perpendicular to B, the solid triangles (circles) give the fit to fw(fT1) in M B terms of bi-Maxwellian functions, and the open triangles give f + f . MB (Equally good fits are obtained if bi-Lorentzian instead of bi-Maxwellian 24 functions are used. ) Two dimensional contours of both velocity distributions are drawn in the bottom half of the figure. Quantitative characteristics of the model fits typically obtained 24 during high speed flows are given elsewhere. Of importance here, is a qualitative discussion of the nature and extent of the free energy carried by solar wind protons near 1 AU. This energy is carried mainly by a A secondary proton beam convecting along B, relative to and faster than a main proton component. This motion is observed in association with a distortion of the velocity distribution of the main component such that its perpendicular temperature, T^M> is larger than its parallel temperature, 21 12 T|JM. ' In addition the beam is generally hotter than the main component and only weakly anisotropic. Although in a gross sense T,, > T,_., most two III) -L D dimensional contour diagrams show evidence that the beam as well as the main
776 component is being heated perpendicular to B. For example both contour diagrams in Fig. 3 show a pronounced perpendicular bowing at high proton energies. c) Alpha Particles Characteristics of alpha-particle velocity distributions measured in the solar wind near 1 AU are known in far less detail than corresponding proton distributions because they are, on the average, only a 5% constituent. Although striking examples of double streaming configurations have been observed on rare occasions most often alpha distributions appear as a single component convecting relative to and in general faster than the protons. , » » , ⢠During high speed flows, the drift speed of the alpha particles is such that they lie roughly, but slightly more than midway 24 between the proton main and beam components in velocity space. In addition solar wind alpha particles are typically four times hotter than the protons near 1 AU. * 3) The Regulation of Solar Wind Heat Flux Near 1 AU Electron heat conduction provides a major means of energy transport in collisionless plasmas. A thorough knowledge of all possible heat flux regulating mechanisms is therefore essential for understanding the behaviour of physical systems containing hot plasmas, Several processes capable of reducing the flux of heat transported through the solar wind have been suggested as applicable within 1 AU of the sun, Most of these processes are either non kinetic in nature or rely critically on assumed plasma conditions which may or may not apply to the inner solar wind. Since in the interest of brevity, the scope of this report is confined to reviewing only those
777 kinetic processes about which detailed plasma measurements are available, many of these suggested heat flux regulating mechanisms will not be 43 covered. A more comprehensive review can be found elsewhere. It now appears likely that at least one of many possible kinetic heat flux regulating mechanisms is active at times in the solar wind near 1 AU. Solar wind plasma and field data can therefore be used to obtain a detailed and quantitative understanding of this and perhaps other such mechanisms. In the following paragraphs the strongest evidence indicating effective heat flux regulation near 1 AU in the solar wind is first presented. This is followed by a review and critical discussion of possible mechanisms proposed to explain the measurements. As mentioned in Section 2a, below several keV energy, solar wind electron velocity distributions can be separated into two relatively convecting, distinct components, f and f . (Note though, that the hot component, f , may often be complex and consist of two distinct parts; one which is relatively isotropic and one which is strongly beamed. ) Heat transport in the solar wind near 1 AU appears to result mainly from the bulk motion of the hot electrons relative to the plasma frame of reference, AV , H Simultaneously, the cold electrons move opposite to AV with relative drift B speed, AV , in such a way that the net electrical current is zero within 23 experimental uncertainties. In other words, the solar wind heat flux, Q , is observed to be proportional to both AV and AV . Consequently, any C H kinetic mechanism capable of limiting either AV or AV will also limit Q .
778 Recent evidence strongly suggests that AV and/or AV are limited by the local Alfve"n speed, V., near 1 All. Not only do variations in AV and AV follow variations in V., but the average magnitudes of AV and V are c A c A 26 closely equal. A remarkably clean example of correlated variations between AV and V. occurring on a fine time scale is shown in Fig. 4. C A Even though the ratio, AV /V., is not constant throughout this particular 12 hour period, inspection of the figure leaves little doubt that variations in AV and V are indeed related. An example indicating a C A correlation between AV and V over a longer time period is reproduced in C A 26 Fig. 5. These examples as well as others have been interpreted to suggest that the Aflven speed is at times a prime regulating factor of the solar wind heat flux through the relation 0 a A V a V.. e c A Theoretical analyses of heat conduction in the solar o/\ f Q f f o *5 o / wind ' ,u ' ' have shown that if AV is ever larger than about V , C i\ one of several microinstabilities may develop depending on the values of various plasma parameters. Assuming model velocity distributions consisting of two relatively convecting electron bi-Haxwellians and one proton bi-Maxwellian, the most important instabilities involve the Alfve*n, magnetosonic and whistler modes. Whereas the Alfve"n mode is driven unstable by the relative motion between the cold electrons and the ions, both the magnetosonic and whistler modes are driven unstable by the o o O / relative motion between the hot electrons and the ions. ' The following grossly simplified overview of solar wind heat conduction near 1 Al l can be synthesized from current measurements and ideas as follows. Near 1 All, heat is carried primarily by electrons with energy greater than about 60 eV, which move away from the sun relative to
779 the solar wind rest frame. This motion is accompanied by a return current of cold electrons in order to prevent a secular charge build up on the sun. As the entire plasma expands away from the sun, solar wind electrons traverse regions of ever decreasing AlfveYi speed so that at some location, AV and/or AV become sufficiently large compared to V C 'I " that one or more of the heat flux instabilities become active. The effect of these instabilities must be to reduce continuously both AV and AV in order to maintain a marginally stable state. If the instability H interacts strongly only with the cold electrons thus reducing AV , then the interplanetary electrostatic potential must increase sufficiently to reduce AV (and hence the heat flux) in order to maintain a zero net H fiQ R ^ 9 *} R? electrical current. ' ' ' It is expected that this reduction is effected both by a direct deceleration of all weakly interacting electrons and a trapping of a small fraction of previously unbound, intermediate energy electrons. However, it is also possible that the instability interacts strongly with the 2 35 hot electrons thus reducing both AVU and the heat flux directly. ' In either H case the flow of heat is continuously regulated by the ever decreasing magnitude of the Alfven speed. Because its phase speed is sufficiently high that solar wind ions cannot interact strongly with its oscillating fields, only the heat flux driven whistler mode has been identified tentatively in solar wind data. This identification has been made primarily in the low speed solar wind when the hot component anisotropy is generally small and f can be adequately H characterized as a single convecting component. Regulation by whistler waves is suggested because AV appears to be correlated with V. only when c A the temperature anisotropy of the hot electrons is low; a result predicted by the linear theory of the whistler heat flux instability. ' This identification does not preclude the possibility that other
780 instabilities are also effective during these and other flow conditions, in regulating the flow of heat in interplanetary space. In fact this latter possibility is suggested by observations of correlated AV -V C A variations in the high speed solar wind as shown in Fig. 5. Although the above overview seems reasonable and is consistent with current knowledge about solar wind electrons near 1 All, a few words of caution are in order. The shapes of both electron and ion velocity distributions are generally more complex than those assumed by theoretical analyses of heat flux regulating mechanisms. Since many of these mechanisms involve resonant instabilities which depend sensitively on the shapes of velocity distributions in the resonant velocity range, the physics of heat flux regulation may be considerably more complicated than the simple picture drawn above. For example, it is not known how effective the heat flux driven whistler instability will be in limiting AV and AV . Ouasilinear theory predicts that growing whistler waves should only modify electron velocity distributions in a very small region 35 of velocity space. Since the free energy available to these waves from such a region is small, in the absence of other active processes stabilization would then be expected to occur at a very low wave level. However, if low level stabilization actually occurs, then sufficient time is not available for the vrtiistler heat flux instability to effectively limit AV and hence the heat flux. This result is contrary to observations. A further indication of the inadequacy of a simple minded picture of interplanetary heat flux regulation comes from measured shapes of solar wind electron distributions. In interplanetary space, electrons
781 above about 2 thermal speeds are generally collisionless (see e.g. Ref. 27). It is therefore difficult to understand 1) why cold electron distributions are so nearly isotropic and Maxwellian out to about 2.5 thermal speeds and 2) why the hot electrons travelling back towards the sun exist at all and appear so isotropic, unless other processes are simultaneously active near 1 AU. We are thus led to speculate that the effectiveness of the whistler and other instabilities in limiting 0 requires either 1) the simultaneous action of other unrelated instabilities 2) generally noisy or turbulent plasma conditions driven by waves of solar origin, or 3) an inhomogeneous medium in which nonlocal processes are fundamentally important. Finally, even if sufficient time is available for the whistler or other instabilities to be effective in limiting AV near 1 AU, a full understanding of heat flux regulation rl requires clarification of the processes which determine the densities and 26 temperatures of f in relation to those of f . It is likely that a basic understanding of the physics of heat conduction in the solar wind requires a fundamentally nonlinear and inhomogeneous theory in which the particle distributions maintain an equilibrium with self-consistent wave fields and continuously adjust to changing plasma conditions as the solar wind convects away from the sun.
782 4) Type III Radio Emission Both the theory and observation of interplanetary Type III radio 1 ft ^ ^ 71 ft / emission have been reviewed recently. ' ' ' These bursts consist of radio waves which drift in frequency from high values above 100 MHz to low values near about 10 kHz. It is now reasonably certain that they are excited at twice the local plasma frequency by solar generated electron beams with peak 4 5 31 52 47 energy between 5 and 100 keV. ' * >-⢠> These observations pose two basic theoretical problems. It is necessary 1) to understand the plasma mechanism which is responsible for converting the energy carried by an electron beam in a low density plasma into energy carried by plasma oscillations without disrupting the beam and 2) to understand the coupling mechanism which converts plasma waves to electromagnetic radio waves. Such an understanding is essential for proper data interpretation in much of radio astrophysics. The basic beam-plasma mechanism responsible for the production of longitudinal electrostatic plasma waves has been known for some time (see e.g. Refs. 71 and 53). However subsequent interactions between the waves and the exciter beam, as well as among the waves, which lead both to beam disruption and electromagnetic radio waves, are not very well understood. For example the most important nonlinear mechanisms which couple a plasma wave to ion density fluctuations and to other plasma waves do not scatter the 13 pump radiation out of resonance with the initial electron beam. This fact has two important consequences. First the insufficiently scattered plasma radiation will react back on the electron distribution in such a way as to remove the free energy which drives plasma waves initially unstable. A marginally stable state will therefore be quickly established. Second,
783 excitation of electromagnetic radiation at twice the local plasma frequency is thought to require two plasma waves travelling in opposite directions. However, a recent three-dimensional calculation shows that the fastest growing wave-wave scattering process does not produce oppositely propagating "1*5 £ / plasma waves " as was thought previously. A resolution of the beam disruption problem has been suggested in terms of spatially bounded and time dependent electron streams as illustrated in Fig. 2. ' ' If true, then plasma waves will be driven unstable in isolated locations in interplanetary space wherever secondary peaks in local electron velocity distributions happen to form. It is then expected that at the various sites of unstable wave growth, quasilinear relaxation processes will act quickly to establish marginally stable states leading to termination of local wave growth. This cycle will then be repeated at other locations in interplanetary space giving the appearance of a continuous and slow removal of energy from the solar generated electron streams. Recently, evidence consistent with this picture has been found using in situ plasma wave 39 A 0 measurements. ' In particular, electron plasma oscillations with sufficient amplitudes to account for the intensity of observed radio waves are observed (although only rarely) in association with solar electron streams. Furthermore when such oscillations are measured they are observed to be intense and intermittent. However, due to as yet unexplained effects, these plasma ascillations have not been observed during the time of rising intensity of electromagnetic waves. At present a theoretical resolution of the second difficulty has no widespread acceptance although current research in this area is quite active. There appears to be no generally accepted mechanism capable of generating oppositely propagating electrostatic plasma waves which subsequently couple
784 to form electromagnetic radio waves at twice the local plasma frequency. 5) Ion Beam Regulation In the past, much theoretical effort (see e.g. reviews in Refs. 68 and A3) has been expended towards understanding kinetic processes effective in limiting the overall thermal anisotropy of solar wind protons. ' " These studies assumed that solar wind proton velocity distributions could be adequately characterized by bi-Maxwellian functions. However, recent, more detailed measurements of solar wind proton velocity distributions have shown that the overall thermal anisotropy of solar wind protons is intimately 21 associated with two component proton configurations. Indeed, most of the time, proton distributions in the solar wind are complex and better described in terms of two relatively convecting components then in terms of a simple bi-Maxwellian (see discussion in section 2b and Ref. 24). An understanding of the radial evolution cf the internal state of solar wind protons therefore seems to require at the least, a thorough knowledge of ion beam driven instabilities in addition to simple anisotropy driven instabilities. Even though a complete treatment of proton distribution shapes must include interactions with the entire solar wind wave field independent of origin, for reasons given in section 1 the following discussion concentrates only on kinetic ion beam regulation mechanisms active in the high speed solar wind near 1 ATI. A comprehensive review of other processes which may be effective in determining the internal state of solar wind protons near 1 AU is given 68,43,14 elsewhere. The initial approach taken towards understanding ion beam regulation relevant to solar wind plasma conditions, arbitrarily separates the problem into two parts. The first assumes various non-equilibrium two component ion configurations in the absence of significant wave fields. The stability limits of various plasma modes are then determined. ' ' ' Next, the second order effects of the growing waves on the initially unstable,
785 spatially averaged velocity distributions are calculated (see e.g. Chapter 12 of Ref. 16 as well as references cited therein, and Ref. 36). This approach provides a description of the evolution of particle velocity distributions and fluctuating fields only during the initial stages of instability. In particular it determines neither the nonlinear saturation mechanisms nor the Vlasov-Maxwell equilibria which are eventually established. A knowledge of the final stationary state requires an exact solution of the nonlinear Vlasov-Maxwell equations (see, e.g. Ref. 1 and references cited therein, as well as Refs. 15 and 3). The solar wind provides an excellent laboratory for studying, in quantitative and nonlinear detail, ion beam regulation in a collisionless, high 3 plasma (g is the ratio of the particle pressure to the background magnetic field pressure). An overview of ion beam interactions in the high speed solar wind based on current measurements and ideas is synthesized in the following paragraphs. For reasons not yet fully understood interpenetrating proton streams are observed in interplanetary space. Since the solar wind expansion sets up conditions such that V decreases with increasing distance above the coronal A base, the relative velocity between interpenetrating proton streams should at some distance become comparable to V . At this point, one of three possible A modes will be driven unstable depending on the parallel $ of the main proton component, g ,. ' If 3 < 0.35, then an obliquely propagating ion cyclotron instability will have the lowest threshold. This instability becomes more field aligned as TIM/TIIM increases. However if 0.35 < ^ < 0.45, an oblique magnetosonic instability has the lowest threshold and above p ^0.45 a field aligned magnetosonic instability has the lowest threshold.
786 The next step in the evolution of solar wind proton velocity distributions is, at present, not understood. Multidimensional theories have not yet been developed but are needed to determine the modifications of particle velocity distributions subject to the action of obliquely propagating, ion-cyclotron and magnetosonic waves. However, since for these distributions, free energy is carried by virtue of the relative streaming between beam and main proton components, it is expected that ion beam driven instabilities should cause perpendicular heating at the expense of relative convection energy. In other words, one expects a faster moving ion species to slow down, a slower moving species to speed up and (Ti/Tii) of all ion components to increase. In particular the damping of ion-cyclotron waves should accelerate alpha-particles in the solar wind up towards the phase speed of the wave. It is not possible to determine the marginally stable states of proton beam driven instabilities from quasilinear theory. Instead, such a determination requires a fully nonlinear analysis. Since nonlinear analyses are very difficult, measured solar wind ion velocity distributions have been consulted for guidance. This procedure is expected to provide the desired solutions because as noted earlier, the time required for the solar wind to expand through a density scale height is long compared to typical e-folding growth times of ion-beam driven instabilities. Indeed, statistical studies of shapes of solar wind proton velocity distributions have indicated the existence of a preferred class of configurations that can be summarized by an 20 empirical closure relation. A subsequent, more detailed investigation has led to the identification of a class of ion velocity configurations which are
787 exact, stationary solutions of the nonlinear Vlasov equation and Maxwell equations. These solutions support a nonlinear ion-cyclotron wave and remove the strong ion-cyclotron wave instability predicted by linear theory ' ' ' which was inconsistent with the persistence of observed proton and alpha-particle velocity distributions in the high speed solar 12 24 wind. " The theoretical and experimental proton velocity distributions consist of two interpenetrating beams convecting relative to one another A along the average magnetic field direction, B . The higher density main component travels slower than the nonlinear Alfve"n wave and has a thermal A A speed perpendicular to B which is larger than that parallel to B . The o o lower density beam component travels faster than the wave and has a thermal speed along B which is larger than that perpendicular to B . Simultaneously, the alpha particles travel faster than the total proton rest frame in such a way that their speed is close to but slower (fascer) than the wave phase speed if (Tj/T|i) is greater (less) than one. A schematic two-dimensional representation of the proton part of this configuration is shown in Fig. 6. 6) In Situ Acceleration of Energetic Particles Viewed from a distance, the heliosphere must appear like a source of energetic particles. Most of these particles are injected with high energy into interplanetary space by acceleration mechanisms active in the lower solar atmosphere. However, several different experimental observations indicate that some of these particles are also accelerated by mechanisms active in interplanetary space (see e.g. Refs. 70, 6, 77, 49, 55 and 56).
788 All such mechanisms are of special interest because they provide clues as to the origin of galactic cosmic rays which carry a non-negligible fraction of 73 the total energy density present in interstellar space. Furthermore one of our windows in astrophysics is in the form of high energy particles. An understanding of particle acceleration mechanisms will therefore help in understanding the physical conditions in the neighborhood of those astrophysical objects which are the major sources of these particles. One of the many possible acceleration mechanisms which, by inference, must operate only in interplanetary space is presented in the next several paragraphs. This mechanism involves the acceleration of interstellar neutral atoms which penetrate into the heliosphere and become singly ionized by either photoionization or charge exchange collisions. Subsequent to ionization, a small fraction of these particles get accelerated by the solar wind up to energies of about 10 MeV per nucleon. Details of the interaction between interstellar neutral atoms and the sun have been reviewed elsewhere and so will not be repeated here (see reviews in Refs. 9, 74, 17 and 44). Instead, we will concentrate on the evolution of singly ionized interstellar atoms after their injection into the solar wind. Particular attention is given to He because it is most abundant and should be representative of the heavier ions such as N , 0 and Ne . The evolution of He velocity distributions subsequent to photoionization is not known. The anisotropic distribution shapes which 19 should evolve in the absence of wave-particle interactions " have been shown 79 41 to be unstable. " Since initial time scales for wave growth are short compared to the expansion time scale, it was postulated that He ions become
789 80 quickly incorporated into the solar wind. However a nonlinear analysis has not been made so that wave saturation levels and consequent energy and pitch angle diffusion times are not known. It is therefore theoretically possible that in addition to the above suggestion, that the He ions 2) evolve 19 76 adiabatically ' , 3) become isotropized but not thermalized by subsequent wave-particle interactions , or 4) are accelerated by transit time damping 28 29 of a spectrum of fast mode waves present in the outer solar wind. ' Only a meager amount of experimental information is presently available to settle this question. Significant concentrations of an ion identified as He were first observed in two solar wind ion spectra. However a subsequent more comprehensive search of solar wind heavy ion spectra yielded only upper limits which were an order of magnitude lower than that expected + 22 if interstellar He ions are quickly thermalized. " Thus although it is possible that occasional solar wind conditions can lead to complete assimilation, most often He velocity distributions must remain diffuse. The first possible evolution sequence mentioned above can therefore not be dominant. On the other hand an anomolous component of energetic ions has been observed in interplanetary space ' ' , and plausibly interpreted ' -4 in terms of the acceleration of a small fraction (10 ) of the initially low energy heavy ion population (including He ) of interstellar origin. These observations seem to favor alternative 4. However, since the number fraction of the ions actually observed with high energy is exceedingly small, a firm decision cannot be made at present. It is likely that the bulk of the ions evolve to some nonlinear stationary state characterized by a high energy
790 extension which is observable to energies up to 10 MeV per nucleon. Future observations which are capable of a unique identification of singly ionized heavy ion species will be necessary to settle this question. 7) Summary and Suggested Future Research Velocity distributions of solar wind electrons and ions are observed to be very complex near 1 AU. Although they depend ultimately on details of the internal state of the plasma in the low corona, they seem to respond to variations in local plasma conditions indicating that often, enough time is available that nonlinear stationary states are locally established. Perturbations from these states excite a variety of instabilities in isolated locations which saturate quickly and nonlinearly to produce new stationary states. Three examples of this process were illustrated in Sections 3 through 5. Sufficient data are not yet available to determine how velocity distributions of suprathermal ions of interstellar origin evolve in interplanetary space but they may evolve similarly. The physics of these and related problems not only have intrinsic interest but they have wide application. 1) An understanding of heat conduction regulating processes is important to both astrophysics and laboratory fusion research because both involve hot, fully ionized, colllsionless plasmas. Not only may heat conduction be a major source of heat loss from the outer atmospheres of the sun and other stars, but also from plasmas magnetically confined in laboratory fusion devices as well as coronae surrounding pellet targets in inertially confined fusion devices. 2) A detailed and quantitative understanding of radio emission mechanisms is
791 essential for interpreting radio astronomical measurements in terms of conditions and processes occurring within some astrophysical objects. 3) An understanding of the evolution and eventual stationary states of ion beams traversing hot tenuous plasmas is of particular interest to fusion research in that use of such beams has been suggested as one way of heating the ambient ions in two component Tokamak devices. In addition, a categorization of nonlinear Vlasov-Maxwell equilibria is of general interest to laboratory fusion research because of the necessity here of long time confinement for economical operation. 4) An understanding and assessment of the importance of all mechanisms leading to particle acceleration is important to the field of high energy astrophysics because information concerning conditions within some astrophysical objects comes in the form of high energy particles. In addition, galactic cosmic rays carry a significant amount of the total energy density which permeates interstellar space and so must be important both to the nature and dynamical evolution of the state of the intersellar gas. The successes achieved during the past five years in solar wind plasma physics point the way, in part, to future efforts. Specific suggested expansions of past work relevant to the topics discussed in this report include the following. 1) Measurement in three-dimensions of solar wind electron velocity distributions should be made on a fine velocity grid for all radial distances inside of 1 AU. In particular, measurements at radial distances as close to the sun as possible as well as over the polar regions will be important for understanding the dynamics of the coronal expansion. 2) The heat flux driven whistler instability should be simulated on the
792 computer in order to understand its saturation mechanism as well as determine the final nonlinear stationary electron state. 3) A search through existing solar wind data should be made for the signatures of other kinetic processes capable of regulating the flow of heat in interplanetary space. Particular attention should be given to interactions with waves of solar origin as well as with those produced by ion driven instabilities. 4) High time resolution measurements of the amplitude and k-vector orientation of plasma waves should be made in interplanetary space (preferably at two radial distances) to understand the mechanism of plasma wave excitation and conversion to produce Type III radio emissions. Time constants as short as 1 msec may be necessary to detect the short plasma wave bursts expected during the rising portion of these emissions. Simultaneous measurements of suprathermal electron velocity distributions should be made in three dimensions with as high a time resolution (snaphot time) as is practicable. It would be of interest to make these measurements simultaneously using two spacecraft with one as close to the sun as possible in order to study the beam evolution and understand the nonlinear saturation and electrostatic to electromagnetic wave conversion mechanisms. 5) High spectral resolution measurements of solar wind ion velocity distributions in conjunction with ion gyroradius and smaller scale wave fields should be extended throughout the inner regions of interplanetary space in order to determine the origin and radial evolution of double ion streams. It is also important to assess the importance of such streams in the transfer of energy from the sun to interplanetary space. In this regard measurements both as close to the sun as is practicable as well as over the solar poles will be of special interest. 6) Theoretical work is needed in order to understand wave-wave
793 coupling mechanisms and their resulting coupling rates, for the general case of obliquely propagating electromagnetic waves. It would then be possible to understand the development of, and assess the importance of, this type of turbulence in the solar wind. In particular it is not known whether the magnetic irregularities so prominently observed in interplanetary space constitute a turbulent spectrum or just plasma noise. It is also not known at what wavelengths energy is fed into the system. In addition, a theoretical effort is needed to extend present work on nonlinear Vlasov-Maxwell equilibria to include the general case of a spectrum of obliquely propagating electromagnetic and electrostatic waves. 7) Detailed measurements in three dimensions should be made of the velocity distributions of as many of the solar wind minor ionic constituents as possible in order to probe the nature of the solar wind wave field. 8) Measurements of ion velocity distributions which are capable of a unique identification of singly ionized suprathermal heavy ion species are needed in order to understand the processes which result in the acceleration of initially neutral atoms, injected into the solar wind from the local interstellar medium. In conclusion, the study of kinetic plasma processes active in the solar wind is a growing field of research which, in addition to its own intrinsic interest, has application to a wide range of laboratory fusion and astrophysics research problems. Recent progress, reviewed in the above sections, has demonstrated this fact. Such progress points the way towards a continuing joint experimental and theoretical effort in understanding some very complex, collective processes, which can occur in any collisionless plasma whether it is produced in a laboratory fusion device or in some astrophysical setting.
794 10s ro 10 ,-26: ~28 io" - IO'30 10 .-32 ^. Imp? electron spectrum 12/13/72 0103 U.T. r -20 -6 HO -5 0 5 10 Electron Velocity (x 10 km/sec) 15 20 FIGURE 1 A cut through a solar wind electron velocity distribution along the magnetic field direction. The two solid parabolas are the two bi-Maxwellian functions which best fit the low and intermediate energy electrons respectively. The vertical lines through the data points indicate the statistical plus digitization er- rors where they are larger than the plotting symbols. FIGURE 2 A one-dimensional schematic il- lustration of how a secondary electron peak in interplanetary space can result from a sud- den and localized deposition of energy in the corona. The upper panel illustrates the effect of heating at time rQ on coronal electron dis- tributions and the lower three panels trace the subsequent evolution of interplanetary electron distributions under the assumption of scatter free propagation of the heated electrons.
795 22 MARCH 1973 0021 UT 0545 UT FIGURE 3 A plot of two typical proton velocity distributions measured during high speed solar wind flow conditions. The lower panels show the two dimensional contour diagrams of the measured distributions and the upper panels compare the best fit rela- tively convecting two component bi- Maxwellian model with the radially pro- jected data. The beam fits are represented by the solid circles, the main component fits are given by the solid triangles, the open triangles give the sum of beam and main component fits, and the measured distribution is plotted by the open squares. 6OO 7OO 800 9OO 6OO 7OO 8OO 900 RADIAL VELOCITY (km s"1) H 600 O o UJ 550 > IMP 6 MARCH 19, 1973 500 450 400 TIME (h.UT) 12 FIGURE 4 A plot of the Alfven speed, VA, relative cold component to total electron population bulk speed difference, AVc, and solar wind speed, Vw, during a 12 hour period centered on the maximum speed gradient region at the front edge of a high speed stream.
796 150 100 600 500 _ o o) 400 10 300 TIME (days) FIGURE 5 Hourly averages of the same parameters plotted in Figure 4 showing their variation through a clean example of a high speed stream. The curve labelled NHAVH/N(, in this figure corresponds to that for AVC in Figure 4. ECLIPTIC PLANE HIGH DENSITY MAIN COMPONENT LOW DENSITY BEAM COMPONENT FIGURE 6 A schematic 2-dimensional representation of proton velocity distributions measured during high speed solar wind flow conditions. The f direction points radially away from the sun and B0 is the direction of the background magnetic field. The vector, VM(VB) is the bulk velocity ofthe main (beam) proton component relative to a reference frame stationary with respect to the sun and V is their relative streaming velocity. The ellipses represent velocity contours of the same constant fraction of the peaks of each of the proton components. Since in actuality, the main component peak is substantially higher than the beam component peak (see Fig. 3), the two elliptical contours drawn here cannot be simply combined to yield a contour^of the total velocity distribution. The symmetry axes of both ellipses in three dimensions are aligned along B0 so that a 3-D contour of the main component is an oblate ellipsoid with a thermal speed perpendicular to B0 larger than that parallel to B0 (door knob shaped) and that of the beam compo- nent is a prolate ellipsoid with a thermal speed parallel to BQ larger than that perpendicular to B0 (cigar shaped).
797 Acknow]ed gmen ts I wish to thank B. Abraham-Shrauner, S. P. Gary, M. L. Goldstein, J. T. Gosling, D. A. Gurnett and D. F. Smith for many useful discussions concerning parts of this review. This work was performed under the auspices of the U.S. Energy Research and Development Administration.
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