Energetic Particles in the Quiet Corona A. MacKinnon 1,2, M. DeRosa 3, S. Frewen 2, & H. Hudson 2 1 University of Glasgow, 2 Space Sciences Laboratory, UC Berkeley, 3 LMSAL Palo Alto

Possible particle sources CRAND (Cosmic Ray Albedo Neutron Decay): Standard radiation-belt mechanism Metric type II/ Moreton shock acceleration: Proposed here, theory unclear SEP capture: Proposed here; known physics for terrestrial belts Microflares/nanoflares: Speculative

Does the solar corona have a dipole field? No, not really! The obvious dipolar structure apparent in eclipse pictures at solar minimum does not relate to a real object The solar-wind field is strongly dipolar, but at the same time highly non-potential (a) SOHO composite at solar Minimum (b) Dipole model fit by S. Gibson Conclusion: can be rather dipolar

Experimenting with a “real” field Schrijver-DeRosa PFSS models provide a first estimate of global field structure for particle motions Within these fields, we follow particle motions in the adiabatic approximation This work does not apply directly to CME situations, except for relatively undisturbed parts of the corona

How stable is PFSS at low order?

Gross consequences of drifts ● Curvature and gradient drift velocity: ● Here we explore potential fields, B = - ∇, so V D ~ ∇ B  ∇ ● A particle's local drift velocity lies in the intersection of the local equipotential and 'isomagnetobar' surfaces. ● Particles with 90  pitch angles, at field minima, drift across the field at constant B and, in the intersection of two such surfaces (cf. 'equatorially mirroring particles' in Earth's radiation belts) ● Particles with arbitrary pitch angles drift within a region defined by B min and B max, and the values of at their mirror points.

equipotential'isomagnetobar' A particle's instantaneous drift velocity will lie in the intersection of these two surfaces. All particles will drift towards z=0 in such localised fields. Part of an idealised field, e.g. of a single active region. Surfaces generated using a single, sub-surface dipole for illustration. solar surface plane height

Example: PFSS, 30 Sept 2006 Figures show contours of B in the plane of the photosphere (left) and in vertical cross-section at fixed latitude (right), from PFSS, for a small, weak active region on 30 September A particle first found in the corona, at the apex of the dotted contour in the right figure will drift and eventually meet the surface somewhere on the dotted contour (same B) in the left figure.

Example: PFSS, 30 Sept 2006 Intersections in the solar surface of equipotentials (dashed contours) and isomagnetobars (solid contours) map onto locations in the corona. A particle of non-zero pitch angle bounces between mirror points and drifts laterally, moving towards a curve in the surface defined by its locus in B and. Note: axes are not labelled in degrees! Fig. is 200,000 by 100,000 km

Particle drifts in an active region This compares the distribution of |B| with the scalar potential  for a weak active region seen in the PFSS maps for 2004/01/14 00:04, evaluated at 1.18 R sun. The drift motions of trapped particles must be be perpendicular to the gradients of each quantity.

Analytical expressions for guiding center motions in a dipole field exist (e.g. Northrop, 1966; Schulz and Lanzerotti, 1974). These may become useful at high altitudes. For non-relativistic protons of energy E (MeV): Here F(  depends on particle pitch angle; 0.67 < F(  The long times over which particles must avoid pitch-angle scattering make solar scale radiation belts unlikely. For a nucleus of atomic and mass numbers Z and A, energy mc 2 on a field line of equatorial height r when the surface, equatorial field strength is B 0, the time to drift once round the Sun is:

Solar Ring Current? Using the expression above, the bounce averaged azimuthal drift velocity is Even particles in the tail of the thermal coronal population will drift. Including only protons above 3v th, integrating over energy and pitch angle and adopting r = 1.5R Sun, n=10 7 cm -3, T=2  10 6 K we find: j  A.m -2 locally modest but implying a total current of order 1 MA. Any more fast particles (e.g. CRAND; low-level QS acceleration; Lorentz rather than Maxwell distribution) would enhance this.

Conclusions We have studied particle transport in the Schrijver-DeRosa PFSS models The solar corona can support partial radiation belts The same methodology can be used for PFSS realizations of active-region fields At present we do not think that solar radiation belts are important, but there are many interesting unexplored possibilities