It is advantageous to regard cosmic rays as the constitutent particles of the Galactic radiation belts and cosmic ray energization as a consequence of inward radial diffusion in the quasi-dipolar Galactic magnetosphere. This process occurs in addition to Fermi acceleration. The purpose of this work is to explore a magnetospheric explanation for the elevation of Galactic charged particles to cosmic ray energies. The magnetosphere that is of interest in this context is not a planetary magnetosphere but a galactic magnetosphere entirely analogous to those inferred from radio observations of distant galaxies. It is the magnetosphere of the Milky Way. Cosmic rays are (by this interpretation) the charged particles that constitute the radiation belts of the Galactic magnetosphere. Thus, the mechanism by which charged particles attain cosmic-ray energies is presumable the mechanism by which radiation-belt particles attain high energies in more familiar magnetosphere, i.e., the radial diffusion associated with magnetic disturbances that contain spectral power resonant with the azimuthal drift of the particles

Luhmann, J. G.

Schulz, M.

English

NASA Technical Reports Server

79
OG 7.2-17
COSMIC-RAY TRANSPORT IN THE GALACTIC MAGNETOSPHERE
Michael Schulz
Space Sciences Laboratory, The Aerospace Corporation
E1 Segundo, CA 90245
USA
J. G. Luhmann
Institute of Geophysics and Planetary Physics, University of California
Los Angeles, CA 90024
USA
ABSTRACT
It is advantageous to regard cosmic rays as the constitu-
ent particles of the Galactic radiation belts and cosmic
ray energizati_n as a consequence of inward radial diffu-
sion in the quasi-dipolar Galactic magnetosphere. This
process occurs in addition to Fermi acceleration.
i. Introduction. The purpose of this work is to explore a magnetospher-
ic explanation for the elevation of Galactic charged particles to cosmic
ray energies. The magnetosphere that is of interest in this context is
not a planetary magnetosphere but a galactic magnetosphere entirely a-
nalogous to those inferred [i-3] from radio observations [4-6] of dis-
tant galaxies. It is the magnetosphere of the Milky Way. Cosmic rays
are (by this interpretation) the charged particles that constitute the
radiation belts of the Galactic magnetosphere. Thus, the mechanism by
which charged particles attain cosmic-ray energies is presumably the
mechanism by which radiation-belt particles attain high energies in more
familiar magnetospheres, i.e., the radial diffusion associated with mag-
netic disturbances that contain spectral power resonant with the azimu-
thal drift of the particles [7].
The existence of galactic radiation belts has been proposed [3]
as a means of explaining the similarity of decimetric (_ 3-GHz) radio-
emission patterns from various galaxies to that from Jupiter's magneto-
sphere [8]. Such radio patterns are believed to result from the syn-
chrotron emissions of relativistic electrons, but it is clear that gal-
axies might (by analogy with Jupiter) have ionic radiation belts (which
" would not be remotely observable) as well as electron radiation belts
(which are). Indeed, it is logical to identify the Galactic cosmic rays
routinely observed in the heliosphere with the constituent ions and e-
, lectrons of the Galactic radiation belts. This identification is sup-
ported (for electrons at least) by comparisons [9,10] between the energy
spectrum of cosmic-ray electrons observed at the top of the atmosphere
and the frequency spectrum of radio emissions from the disk of the Gal-
axy.
2. Field Model. An immediate corollary of this line of thought is that
cosmic-ray energization must be considered within the context of a spe-
cific model for the Galactic magnetic field. A dipolar model [ii] is
convenient and (in view of the radio observations cited above) at least
topologically realistic. The analytical representation of the adopted
field model is
https://ntrs.nasa.gov/search.jsp?R=19850026571 2020-03-20T16:49:04+00:00Z
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OG 7.2-17
_/2r 3) _._ sin 8)Bc,
B(r,e) = c (1)
_-_ZBC = (_'_cos 8 - _8 sin 8)Bc, r < rc
where r is the radial coordinate, 8 is the colatitude, z = r cos 8, r
is the radius of the Galactic core, and Bc (425 nT) is the magnltudeCof
the (ideally uniform) magnetic field within. The emitting electrons in
this model [3] reside mainly near the magnetic equator (cos 8 = 0) and
not near the magnetic axis (sin 8 = 0), in contrast with the assumption
of other investigators [11,12]. It is convenient to define the (dimen-
sionless) magnetic-shell parameter
(r/rc)CSC2@, r _ r _ 2 kpc
L = c (2)
(rc/r)2csc28, r 5 r _ 2 kpcc
in analogy with the L parameter encountered in the study of planetary
magnetospheres. It follows from (2) that L a i. A more realistic model
of the Galactic B field would entail a more widely distributed azimuthal
current, which in (i) is confined to the sphere r = rc. The dynamo, cur-
rent of a real galaxy would presumably involve the entire core, as well
as a major part of the disk. The disk current would tend to distort
magnetic shells by analogy with the "magnetodisk" model [13] of Jupi-
ter's outer magnetosphere. This distortion would account for observa-
tions [i0] that suggest a B field parallel to the disk itself, while
preserving the generally poloidal form [11,14] of the large-scale Galac-
tic magnetic field. Moreover, energy-density considerations [i0] sug-
gest that cosmic-ray ions themselves must generate (through gyration and
adiabatic charged-particle drifts) a Galactic ring current that signifi-
cantly distorts magnetic shells from dipolar form even beyond the disk.
It is convenient nevertheless to adopt a dipolar model of the Galactic B
field in order to discuss a first approximation of cosmic-ray kinematics
and transport in the Galactic magnetosphere, just as it is customary to
adopt dipolar models of planetary magnetic fields in order to study ra-
diation belt dynamics for the earth and Jupiter.
3. Kinematics. The adiabatic theory of charged-particle motion there-
fore provides a kinematical framework for understanding the transport of
cosmic-ray ions and electrons in the Galactic magnetosphere, just as it
does for radlation-belt particles in planetary magnetospheres. Adiabat-
ic theory is based on quasi-conservation of the three invariant quanti-
ties M, J, and _, which are proportional (respectively) to the action
integrals Ji associated with gyration (i=l), bounce motion (i=2), and
azimuthal drift (i=3). The corresponding frequencies _i/2_ associated
with adiabatic charged-particle motion are supposed to satisfy the in-
equalities _I >> _2 >> _3' and so it follows that the adiabatic theory
holds only for particle energies E E 1018 eV/charge on the drift shell
(L = Le _ 5; see below) that supplies Galactic cosmic rays to our helio-
sphere. The bounce period for a very relativistic particle trapped on
this drift shell, which has a radius _i0 kpc (_5 rc; see above) is
2n/_2_105 yr in the dipolar model. Gyration and drift periods are of
this order for particle energies E _ 7XI0 eV/charge if the Galactic
magnetic field has a local magnitude B -- 0.i nT here, and so the adia-
81
OG 7.2-17
batic theory o_8charged-particle motion applies only to particle ener-
gies E << 7 × 10 eV/charge in our part of the Galaxy.
4. Transport and Ener$ization. Adiabatic motion impels a charged parti-
cle to remain attached to its original magnetic shell, i.e., to retain
its original value of L. The usual mechanisms for radial transport of
energetic charged particles in planetary magnetospheres involve time-
dependent disturbances having azimuthal asymmetry. Such disturbances
typically conserve the first two adiabatic invariants M and J while vio-
lating the third invariant _. The result is a diffusion of the guiding
center with respect to L and a corresponding change in the energy of the
particle. The change in particle energy for L >> 1 is conveniently ex-
pressed by the relationship
-3/2 _ (8 in p/8 In L)M, J _ -i, (3)
where p is the scalar momentum of the particle. The precise value of
(_ in p/8 in L) M _ depends upon the L value and equatorial pitch angle
s 0 [15], but the'_imiting values -3/2 and -i in (3) are attained for s 0
= _/2 and s 0 = 0, respectively.
The observed isotropy of cosmic-ray ion distributions in momentum
space [i0] is presumably a consequence of anisotropy-destroying plasma
instabilities [16-19]. The mean value of (a in p/a in L)M j for a fully
isotropic distribution of charged particles trapped in a dipolar magnet-
ic flux tube is found [20] to be
<(8 in p/8 in L)M,j> _ -4/3 (4)
for L >> I. This result suggests the utility of a quasi-invariant object
A m (p2/moBc)n8/3 (5)
for the treatment of radial transport in the presence of strong pitch-
angle diffusion, in preference to the "invariant" A m (p2/moBc)L3 im-
plicitly proposed by Walt [21] for a similar purpose. Indeed, the ap-
propriate exponent for L in (5) is a function of the anisotropy of the
pitch-angle distribution, the values 8/3 and 3 being appropriate to
isotropy and to extreme anisotropy (sO = _/2 for all particles), respec-
tively. The essential point is that particles in a galactic radiation
belt gain (lose) energy by diffusing inward (outward) in L.
The particle energiZation implicit in (5) corresponds to the
mechanism [22,23] typically invoked for radial transport of the highest-
energy particles in the earth's radiation belts. It is separate and
distinct from the well-known mechanism of Fermi [24], which requires the
violation of J for the energization of particles [25] in a dipolar B
field. Both energization mechanisms must rely (in this context) on
pitch-angle diffusion (implicitly at nearly fixed p) to maintain the de-
sired pitch-angle isotropy. Both energization mechanisms are multiplic-
ative in the sense that a particle's rate-of-change of p is proportional
to p itself, among other factors.
5. Source Distribution. Cosmic rays are presumed to originate in (e.g.,
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OG 7.2-17
supernova) events distributed with uniform probability density through-
out the core of the Galaxy. In this model the rate-of-production of
cosmic r_ys per unit volume of magnetosphere turns out to be proportion-
al to L -" for L >> _. However, if the differential energy spectrum is
proportional to p- .6 [I0], then it follows (assuming immediate isotro-
pization) _hat the source of phase-sp@ce deDsity (dlfferenti@_.glux di-
vided by p_) at fixed A varies as L-_(p-Z'°/pZ), i.e., as Loz/Ib, for
L >> i. This is a monotonically increasing function of L, and so it
seems that the net result of radial diffusion in the Galactic magneto-
sphere can be an inward transport of phase-space density, which corre-
sponds via (5) to a net energization of particles subsequently observed
as cosmic rays at L = L® _ 5.
6. Acknowledgements. The work of one author (M.S.) was supported by the
Aerospace Sponsored Research (ASR) program of The Aerospace Corporation.
Both authors thank Prof. F 0 Coroniti for the further suggestion thatcosmic rays of energy E _ i _ eV/charge might (by analogy) be the radi-
ation belt particles trapped in the magnetosphere of the Local Group,
i.e., of the cluster of galaxies to which our Galaxy belongs.
References
i. van der Laan, H., (1975), Eos, Trans. AGU, 56, 433.
2. Russell, C.T., (1976), in D.J. Williams (ed.), Physics of Solar
Planetary Environments, pp. 526-540, AGU, Washington, D.C.
3. Luhmann, J.G., (1979), Nature, 282, 386.
4. Moffett, A.T., (1966), Ann. Rev. Astron. Astrophys., 4, 145.
5. Rudnick, L., and Owen, F.N., (1976), Astrophys. J., 203, LI07.
6. Burch, S.F., (1979), Mon. Not. Roy. Astron. Soc., _186, 293.
7. F_ithammar, C.-G., (1965), J Geophys. Res., 70, 2503.
8. Berge, G.L., (1966), Astrophys. J., 146, 767.
9. Kraus, J.D., (1966), Radio Astronomy, McGraw-Hill, New York.
i0. Longair, M.S., (1981), High Energy Astrophysics, pp. 271, 256, 328,
119, Cambridge Univ. Press, Cambridge, England.
ii. Greyber, H.D., (1965), in I. Robinson et al. (eds.), Quasi-Stellar
Sources and Gravitational C011apse, pp. 389-390, Univ. of Chicago Press.
12. Alfv_n, H., (1981), Cosmic Plasma, p. 57, Reidel, Dordrecht.
13. Hill, T.W., et al., (1974), Geophys. Res. Lett., _, 3.
14. Yusef-Zadeh, F., et al., (1984), Nature, 310, 557.
15. Schulz, M., and Lanzerotti, L.J., (1974), Particle Diffusion in the
RadiatiOn Belts, p. 21, Springer, Heidelberg.
16. Cornwall, J°M., (1965), J. Geophys. Res., 70, 61.
17. Cornwall, J.M., (1966), J. GeophyS. Res., 71, 2185.
18. Scarf, F.L., et al., (1967), J. Geophys. Res., 72, 993.
19. Wentzel, D.G., (1968), Astroph_s J., 152, 987.
20. Hill, T.W., et al., (1983), in A.J. Dessler (ed.), Physics of the
Jovian Magnetosphere, pp. 353-394, Cambridge Univ. Press.
21. Walt, M., (1970), in B.M. McCormac (ed.), Particles and Fields in
the Magnetosphere, pp. 410-415, Reidel, Dordrecht.
22. Kellogg, P.J., (1959), Nature, 183, 1295.
23. Parker, E.N., (1960), J. Geophys, Res., 65, 3117.
24. Fermi, E., (1949), Phys. Rev., 75, 1169.
25. Parker, E.N., (1961), J. Geo_hys. Res., 66, 693.


Cosmic-ray transport in the galactic magnetosphere

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