Hydrodynamic mechanism of solar corona expansio

Samokhin, M. V.

English

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National Aeronautics and Space Administration 
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ST- PF- 10596 '* 
3 - ON THE ORIGIN OF THE SOLAR WIND >/ 
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https://ntrs.nasa.gov/search.jsp?R=19670017083 2020-03-12T11:21:50+00:00Z
ST-PF-10596 
ON THE ORIGIN OF THE SOLAR WIND 
Kosmicheskiye Issledovaniya 
Tom 5, vypusk 2 ,  305-6, 
Izdatel'stvo '"AUKA", 1967 
S U M M A R Y  
by M. V. Samokhin 
The hydrodynamic description of solar corona expansion is retained 
by utilizing for larger ranges the microscopical model and kinetic equa- 
tions, when the length of the free path A e r ,  - r being the characteristic 
scale of the problem. 
* 
* * 
A hydrodynamic mechanism of solar corona expansion was proposed and 
worked out in detail in ref. [l - 41 . 
tion is applicable only for a small length of the free path 
- r is the characteristic scale of the problem. 
crease, this inequality is disrupted already as near as at a distance of 
several solar radii. 
should be described with the aid of microscopical model and kinetic equations. 
However, the hydrodynamic descrip- 
I s r ,  where 
Because of rapid density de- 
This is why, generally speaking, a further expansion 
Assume that in a spherical system of coordinates,+r, 8 ,  4~ with polar 
axis directed along the Sun's angular velocity vector w and with origin at 
the center of the Sun, the interplanetary magnetic field 'B may be locally 
approximated by the Archimedes spiral [ 51 
where Bo = Bo@)  is an arbitrary function of the angle 8 ,  u is the constant 
rate of corona radial expansion. 
thc magnetic field is the result of expansion of an ideally conducting plasma 
with constant radial velocity and of Sun's rotation under condition of axial 
symnetry. 
the expression 
E = - (ilc) [ull], 
whereupon the element of plasma volume is "glued" to the line of force, moving 
As is well known, such a-distribution of 
In a fixed system of coordinates the electric field is given by 
r* i 
sO~C"oG0 
with a velocity f = [wr], so that the component: of velocities w and u across 
f i e ld  may also be represented in the form 
the magnetic line of force are identical: \v1 - + -  ul. This is why the electric 
-f 
E =  - (l/c) $61 , 
A separate charged particle undergoes drifting under the action of the elec- 
tric, gravitational and nonuniform magnetic fields. 
particles of nonrelativistic energies, the principal drift is the one in cros- 
sed electric and magnetic fields, whereas the drift conditioned by the inhomo- 
geneity of the maLgnetic field and the gravitational drift are negligibly small. 
It may be shown that for 
Fig. 1 
Since the fields do not depend on time, the energy is the integral of the 
motion, so that, finally, the drift equations take the simple form 
is where VII /the velocity component along the unitary vector h' = @B, M and IJ are 
the mass and the magnetic moment of the proton,Eo = M v $ / Z  and vo is the ini- 
tial energy ,and the initial velocity of the proton at the distance ro from the 
Sun, go =MGM /ro , 
constant. 
for the meridional drift velocity is negligibly small. 
relations (l), we may represent expressions (2) in the following fonn: 
Mo and G being the mass of the Sun and the gravitational 
The electrostatic potential is rejected in the second formula (Z ) ,  
Taking into account 
Introduced here are the dimensionless quantities a = U I O  IUO.  B = (ora  / 18)  sin 0, y = 
( i l ) t q l  / I ' n )  5111 0. n - = c ~ o  / rnvoz, T = r / ro, where v0 is the component of the initial velo- 
city across the magnetic line of force. -L 
Assume that r,, - m ~ )  =. 2,08.i01 - 4.107 cM,/sec. We shall find the velocity 
of t h c  proton, having outflown with inf-5ial energy €0, a t  the distance of 
Farth's o rb i t ,  that  is for  r = 1 .5  10 
the term ( ~ * / T ~ ) ~ ~  i n  (3) is negligibly small. 
transvmecomponent of proton velocity "u does not depend on the ini t ia l  velo- 
c i ty ,  and the longitudinal component vli is determined by the i n i t i a l  energy 
and, a t  great distances it is not dependent on the magnetic moment. For a 
low-energy proton the motion velocity is perpendicular t o  the magnetic l ine  
of force, since the i n i t i a l  energy passes in to  the potential  energy, while fo r  
a high energy proton the motion velocity is directed along 8. The intenne- 
d ia te  cases are shown in  Fig. 1. The angle cp = arc k (uF/ V r )  is plotted in  ordina- 
tes i n  degrees and the i n i t i a l  energyEo of the proton, o r  e - M ( u , * + v , z ) ; a  kev - i n  abscissa. The dependence + ( E O )  is i l l u s t r a t ed  by the curve I ,  the depen- 
dence +(E) - by the curve 11. 
energy 0.83 kev move radially (such an energy corresponds to  the velocity of 
400 h/sec) .  
an. A t  such a distance from the Sun 
I t  is easy t o  see tha t  the 
As should have been expected, protons with 
Manuscript received on 23 July 1966 
REFERENCES 
1. E. N. PARKER. Planetary Space Sci.,  1 2 ,  451, 1964. 
2. E. N. PARKER. Astrophys. J., 132, 821,  1960. 
3. E. N. PARKER. Ibid. 139, 72, m4. 
4.  E. N. PARKER. Ibid. m, 93, 1964. 
5. D. STERN. Planetary s c e  Sci. 1 2 ,  961, 1964. -
CONTRACT NO. NAS-5-12487 
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'rei: 223-6700; 223-4930. 
Translated by ANDRE L. BRIGIANT 
on 27 April 1967 
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On the Origin of the Solar Wind

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