Abstract

The Role of Alpha Particles in the Emission of Plasma Waves Inside Solar Ejecta

S. Dasso^1,2, F.T. Gratton¹, and C.J. Farrugia³

¹ Instituto de Física del Plasma, CONICET - FCEyN/UBA,

Ciudad Universitaria, Pab.1, 1428 Buenos Aires, Argentina

² Instituto de Ciencias, Universidad Nacional de General Sarmiento,

Campus Universitario, José M. Gutiérrez entre José L. Suárez y Verdi,

1613 Los Polvorines, Prov. de Buenos Aires, Argentina

³ Institute for the Study of Earth, Oceans, and Space,

University of New Hampshire, Durham, NH 03824, USA

Received on 26 December, 2001

I Introduction

Solar ejecta (also coronal mass ejections, CMEs) are a heterogeneous set of objects with the following plasma properties: (i) low proton plasma beta (see [1] and references therein), (ii) bidirectional streaming (along field lines) of suprathermal electron heat fluxes (few hundreds of eV)[2] and energetic protons (~ 1 MeV)[3], (iii) a variable n_a / n_p relative proton-to-alpha particle density which may be much higher than the average solar wind value of ~ 4 % [4, 5], and (iv) a thermal anisotropy (A = T_||/T_^ - 1) which is often negative i.e., T_|| > T_^, for both protons and electrons (see Richardson et al., 1997[6] and references therein). The last two properties may hold only in parts of the ejecta. Although physical parameters of CMEs evolve as they propagate away from the sun, they change little on a timescale of several hours. The excitation of right-hand polarized electromagnetic ion cyclotron waves (EICWs) depends sensitively on a number of parameters: the proton beta (b_p = 8 pn T_p/ B²), the alpha-proton temperature ratio (T_a/T_p), the alpha-proton density ratio (h_a = n_a / n_p), the thermal anisotropy of each specie (A_p = T_{||, p}/T_{^, p}-1, for protons, with similar definitions for alpha particles and electrons), and the electron-proton temperature ratio (T_e/T_p).

The possibility of right-hand polarized wave activity in CMEs due to the negative proton anisotropy was studied in Farrugia et al., 1998 [7], Gratton et al., 1998 [8], Dasso et al., 1999 [9], Dasso et al., 2000 [10], and Dasso et al., 2001 [11]. Here, we focus on the influence of A_a and h_a on the growth (and absorption) rates of the waves. The former is a little known parameter not yet routinely measured in CMEs. However, on the basis of magnetic moment conservation in an expanding magnetic field, we expect that all particle species will develop a negative thermal anisotropy. Thus, it seems plausible that A_a will have the same sign of A_p, i.e., negative in most solar ejecta. The excitation of right-hand polarized EICWs is due to anomalous Cherenkov emission, and relies on a small number of ions (in the Maxwellian tail) that resonate with the wave[12]. As we shall show, there are frequency ranges where emission overcomes absorption for negative anisotropy. Thus, a negative A_a, and h_a, contribute directly to the growth rate. However, the effect of h_a is mostly indirect: adding a increases the inertia of the plasma and thereby reduces the phase velocity of the wave. Thus, more ions (protons and alphas) are brought into resonance. This leads to a considerable enhancement of EICW activity in helium-rich plasmas with respect to low h_a configurations.

II Dispersion Relation

The instability of right-hand polarized EICWs propagating parallel to the magnetic field is described by the kinetic dispersion relation (see, for example [13]),

(summed over species indexed by s= electrons, protons, and alphas; angular frequency w [w = w_r + i g]; wavenumber parallel to the ambient field k; cyclotron frequency W; plasma Zeta function Z). In (1), all species are modelled by biMaxwellian distribution functions. Here, w_ps is the plasma frequency; w_|| = , is the thermal speed (temperature in energy units and m is the mass of the particle); and c is the speed of light. Wave quantities vary as exp[i(k z -wt)], where the z axis is aligned with the magnetic field.

In the following, frequencies and growth rates are normalized to the proton cyclotron frequency x=w/ W, where W = e B₀ / m_pc (B₀ is the background magnetic field intensity); and the normalized wavenumber y = k v_a / W, where v_a=B₀ / is the proton Alfvén velocity. For a plasma composed of protons, alphas, and electrons, Eq. (1) can be written as

The following parameters b_{||, p}=8 pn_pT_{||, p}/, b_{||, a}=(8 pn_pT_{||, a} / )(m_p/m_a), and b_{||, e}=8 pn_eT_{||, e} / , m = m_e/m_p, and h_e=n_e/n_p have been introduced. We solve the dispersion relation numerically using an inhouse code for the Zeta function. Parameters are obtained from statistical surveys[2, 6] and other case studies. From the roots of the dispersion relation, we obtain the complex dimensionless frequency x = x_r + i g, as a function of the wavenumber y.

III Results

The parameter n_a / n_p in CMEs is highly variable[2, 6], with n_a / n_p ranging from very small to values as high as ~ 15-20 %[5]. We consider variations of A_a around moderate A_p values, chosen here in the range T_||/T_^ = 2 - 3. Results of alpha particle effects on the growth and absorption rates of the EICW instability are presented in figures 1-4. Fig. 1 shows from top to bottom the absorption and emission ranges, and the phase speed, all shown as a function of h_a, which parametrizes the various curves. We show results for h_a = 0, h_a = 0.04, h_a = 0.08, and h_a = 0.15. The electrons are isotropic, A_e = 0. The other parameters are A_p = A_a=-0.67, b_p = 0.4, and T_a/T_p = 4. An increase in h_a increases growth rates and shifts the active range to lower frequency. When h_a = 0.15, the maximum value of the growth rate is g/W = 8x10^-4 which occurs for w/W = 0.56. This corresponds to an e-folding time (t) of 15 minutes for a 15 nT magnetic field. Since typical CMEs evolution times are many hours, this t value is sufficiently short to allow the instability to develop.

When the absolute value of the alpha particle thermal anisotropy is increased with respect to the case A_a = A_p, an enhacement of growth rates and a broadening of the emission range ensues. In fact, an increment of the parallel temperature of the alpha particles, keeping the average temperature (T_a/T_p = 4) constant, increases b_{||, a}, which in turn augments the instability. This effect can be observed in the Fig. 2, where we vary A_a (=-0.5, -0.58, -0.67, -0.75) while keeping other parameters fixed at A_p = -0.67, b_p = 0.4, T_a/T_p = 4, h_a = 0.15. Again A_e = 0. For A_a = -0.75, the maximum growth rate is g = 2x10^-3, and the unstable x_r interval extends from ~ 0.2 to ~ 1.8. Conversely, when A_a/A_p is smaller than 1, the active range is reduced and the low-frequency cut-off of the absorption is shifted to lower frequencies. For example, when A_a / A_p decreases by ~ 14 %, from A_a / A_p = 1 to A_a / A_p=0.86, the beginning of the absorption range is shifted to x_r ~ 0.9. At x_r = 1, we find instability with a growth rate g = 3.5x10^-4 when A_a = A_p = -0.67. When A_a = -0.58, at the same frequency we find absorption instead, with damping rate -g = 5x10^-5.

We include the contribution of anisotropic electrons in figures 3 and 4. Fig. 3 shows a case in which the instability is eliminated (and we obtain absorption instead) when A_a goes from A_a = -0.5(=A_p) to A_a = -0.4 keeping A_p = -0.5, b_p = 0.4, T_a/T_p = 4, h_a = 0.08, T_e = T_p, and A_e = -0.5 constant.

Somewhat larger absolute values of anisotropies are considered in Fig. 4. Here, we choose A_a = -0.4, -0.5, -0.67, -0.75, for a configuration with A_p = -0.67, b_p = 0.4, T_a/T_p = 4, h_a = 0.08, T_e = T_p, and A_e = -0.67. A gap in the unstable range (second panel) is formed when A_a=-0.4. In this gap an absorption band appears.

IV Conclusions

Summarizing, we examined the effect of variations in thermal anisotropy and abundance of alpha particles on the growth and absorption rates of EICWs in parameter regimes typical of many CMEs. Increasing n_a / n_p and/or the alpha-to-proton anisotropy ratio produce enhancements of growth and absorption rates. An increment of n_a / n_p also shifts the active range to lower frequencies. When the ratio of alpha-to-proton thermal anisotropy increases, an absorption band may appear between two unstable ranges. To advance studies like the one reported here, it would be desirable to measure the alpha particle thermal anisotropy routinely in CMEs, since as we have shown the right-hand polarized EICW instability is very sensitive to this parameter. The alpha abundance also influences the growth rate by its effect on the phase velocity of the waves. These properties may help to explain the spectrum of low frequency fluctuations seen in many CMEs by WIND at 1 AU [14].

Acknowledgments

Work partially supported by Argentinian grants UBACyT (TX032/98 and X059/2001) and CONICET PIP 4536/96, and USA NASA grant NAG5-2834 and living with a star grant NAG5-10883.

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