Definite evidence for particle acceleration in the solar wind came around a decade ago. Two likely sources are known to exist: particles may be accelerated by the turbulence resulting from the superposition of Alfven and Magnetosonic waves (Statistical Acceleration) or they may be accelerated directly at shock fronts formed by the interaction of fast and slow solar wind (CIR's) or by traveling shocks due to sporadic coronal mass ejections. Naurally both mechanisms may be operative. In this work the acceleration problem was tackled numerically using Helios 1 and 2 data to create a realistic representation of the Heliospheric plasma. Two 24 hour samples were used: one where there are only wave like fluctuations of the field (Day 90 Helios 1) and another with a shock present in it (Day 92 of Helios 2) both in 1976 during the STIP 2 interval. Transport coefficients in energy space have been calculated for particles injected in each sample and the effect of the shock studied in detail

Moussas, X.

Neubauer, F. M.

Quenby, J. J.

Schwenn, R.

Valdes-Galicia, J. F.

English

NASA Technical Reports Server

182
SHOCK AND STATISTICAL ACCELERATION OF ENERGETIC PARTICLES
IN THE INTERPLANETARY MEDIUM
Vald6s-Galicia,J.F.I,Moussas,X.2,Quenby,J.J.S,Neubauer,F.W,Schwenn,R.S
I. Instituto de Geoflsica,UNAM,04510 Coyoac_n,D.F.,M6xico
2. Astrophysics Lab.,National Univ.of Athens,Panepistimiopolis,GR 15771
Athens, Grace.
3. The Blackett Lab.lmperial College, London SW7 G.B.
4. Inst. fur Geophysik und Meteorologie, Univ. K#ln, F.R.G.
5. Max P1anck Inst. fur Aeronomie, Katlenburg-Lindau, F.R.G.
I. Introduction. Definite evidence for particle acceleration in the
solar wind came around a decade ago (Mc Donald et al, 1976,Barnes et al,
1976). Since then a considerable amount of data have been taken at dif-
ferent distances from the sun confirming and extending the first
findings and it is now widely accepted that particles are accelerated in
the Solar Wind (Quenby, 1983). Two likely sources are known to exist:
particles may be accelerated by the turbulence resulting from the super-
position of A1fv_n and Magnetosonic waves (Statistical Acceleration) or
they may be accelerated directly at shock fronts formed by the interac-
tion of fast and slow solar wind (CIRSs) or by traveling shocks due to
sporadic coronal mass ejections. Naturally both mechanisms may be ope-
rative.
Shock acceleration has been widely investigated theoretica11y
(Axford, 1981 and references therein) and there is substantial evidence
of this as an operative mechanism in the HeIiosphere (Scholar, 1984).
However there are also experimental observations not obviously consistent
with shock acceleration v.g.(Van Ness et al, 1984) and some ion enhan-
cements only explained in terms of statistical acceleration (Richardson,
1984).
Previous treatments of statistical acceleration involved
theoretical methods based on power spectral representations of the elec-
tromagnetic field (see Quenby, 1983 and references therein).
In this work the acceleration problem was tackled numerically
using Helios I and 2 data to create a realistic representation of the
Heliospheric plasma as will be described in the next section. Two 24
hour samples were used: one where there are only wave like fluctuations
of the field (Day 90 Helios I) and another with a shock present in it
(Day 92 of Helios 2) both in 1976 during the STIP II interval. Transport
coefficients in energy space have been calculated for particles injected
in each sample and the effect of the shock studied in detail,
2. Interplanetary Medium Model. The magnetic field used is defined from
Bi three dimensional vectors where each one corresponds to the 8 sec.
measurements of Helios I or 2, Every point in space is also furnished
with a solar wind velocity vector Vi where these are the corresponding
velocities in the solar wind frame_ Consequently because all parts of
the solar wind are moving there is an electric field Ei=-Vi x Bi
associated to every point in soace. For every sample we have divided
the space in a series of layers where both the electric and magnetic
fields are constant. Trajectories are integrated based on analytical
182 
SHOCK AND S ATISTICAL ACCELERATION OF NERGETIC PARTICLES 
IN THE INTERPLANETARY MEDIUM 
Valdes-Galicia,J.F.l,Mo~ssas X.2,Quenby,J.J.3,N ubauer,F. 4 ,Schwenn,R. s 
1. Insti uto de Geoffsica,UNAM,04510 C yoac~n,D.F.,Mexico 
2. Astrophy ics Lab.,National Univ.of Athens,Panepistimiopol is,GR 15 71 
Athens, Grece. 
3. The Blackett Lab. Imperial Coll ge, London SW7 G.B. 
4. Inst. fUr Geophysik und Meteorologie, Univ. K61n, F.R.G. 
5. Max Planck Inst. fUr Aeronomie, Katlenburg-Lindau, F R.G. 
1. Introduction. Definit  evidence for particle acceleration in the 
solar wind came around a decade ago (Mc Donald et aI, 1976,Barnes et aI, 
1976). Since then a considerable amount of d ta have been taken at dif-
f rent distances from the sun confirming and extending the first 
findings and it is no  widely accepted that particles are acc lerated in 
the Solar Wind (Quenby, 1983). Two likely sources are known to exist: 
particles may be accelerated by the turbulence resulting from the super-
position of Alfven and Magnetosonic waves (Statistical Acceleration) or 
they may be accelerated directly at shock fronts formed by the interac-
tion o  fast and slow solar wind (CIRls) or by traveling shocks due to 
sporadi  c ronal mass jections. Naturally both mechanisms may be ope-
rative. 
Shock acceleration has been widely investigated theoretically 
(Axford, 1981 and r f rences th rein) and th re is substantial evidence 
of this as an operative mechanism in the Hel iosphere (Scholer, 1984). 
However th re are also experimental observations not obviously consistent 
with shock acceleration v.g.(Van Ness et aI, 1984) and some ion enhan-
cements only explained in terms of statistical acceleration (Richardson, 
1984). 
Previous treatments of statistical acceleration involved 
theoretical methods based on power spectral repr sentations of th  lec-
tromagnetic field (see Quenby, 1983 and r f rences th rein), 
In this work the acc leration problem was tackled numerically 
using Hel ios 1 and 2 d ta to create a real istic repr sentation of the 
Heliospheric plasm  as will be described in the next section. Two 24 
hour samples were used: one where th re are only waVe like fluctuations 
of the field (Day 90 Hel ios 1) and another with a shock pr sent in it 
(Day 92 of Helios 2) both in 1976 during the STIP II interval. Transport 
coefficients in nergy space have been alculated for particles injected 
in each sample and th  ffect of the shock studied in detail. 
2. Interplanetary Medium Model. The magnetic field used is defined from 
Bi three dime sional vectors wher  each one corresponds to the 8 sec. 
measurements of Helios 1 or 2. Every point in space is also furnished 
with a solar wind velocity vector Vi where these are the corresponding 
velocities in the solar wind frame~ Cons quently because all parts of 
the solar wind are moving there is an electric field Ei=-Vi x Bi 
associated to very point in soace. For very sample-we have divided 
the space in a s ries of layers where both the electric and magnetic 
fields are constant. Trajectories are integrated based on nalytical 
https://ntrs.nasa.gov/search.jsp?R=19850026458 2020-03-20T17:02:23+00:00Z
163 SH-1,5,1,
solutions of the equations of motion for each layer. For more details
see Houssas et a1,(1982),
Because we require layers of roughly 1/20 of a cyclotron radius
only 1OO MeV protons have been used in this work, lower energies
require smaller 1MF sampling time to keep a reasonable number of layers
per gyroradius.
3. Calculation of Transport Coefficients in Energy Spaceo First and
second order coefficients (DT and DTT) were calculated in energy space
by two different techniaues. One is based upon the construction of a
steady state distribution by injecting particles with a single energy
To (100 MeV in this case) and removing them when they reach any of the
two preset boundaries "above I' and "below Ij the inJection point (see
Houssas et al, 1982 for details).
Another method is based upon the time evolution of the energy
distribution. D_ is calculated via a least square fit of succesive
distributions first order momenta vs. time. If we take the diffusion
equation in energy, integrate for injection at T=To, assume a first
order Taylor expansion in energy for DTT , and make a determination of
the spread <(T-<T>)2> we arrive at
<(T-<T>)2> = 2DTT(To)t+2(DT )2
from where DTT can be calculated.
Both methods are generalizations of those initially developed
by Jones et al (1978) to study pitch angle scattering on a randomly
generated IMF.
The effect of the shock is traced by counting every particle
encounter with it and recording the resulting energy change. The
average energy change is given by the ratio of the total gain and the
number of shock encounters. Transport coefficients can be calculated
using the time an average particle takes to get back to the shock
t_ = 2X/v where X = mean free path = 0.03 AU (see Valdds-Galicia et al,
I_84) and v = particle velocity.
4. Shock Characteristics. The shock used in this study passed
through Helios 2 on day 92 of 1976 when the spacecraft was at 0.45 AU
from the Sun. It is a perpendicular shock OB_ = 89 ° (Lepping et al,
1971) with a high Alfv_n Mach number MA = 7,5, The magnetic field
overshoot is some 24 Gammas which is around 50% of the downstream
field.
It was assumed to be a plane shock and data were transformed
to a frame where the Y-E plane coincides with that of the shock so
that it is parallel to our layer planes.
3 H .. t . .1, 
solutions of the equations of otion for each layer. For ore etails 
 Moussas t l,(1982). 
Because we require layers of roughly 1/20 of a cyclotron radius 
ly 00 e  rotons    i  t is rk, l er ergies 
require s aller 1 F sa pling ti e to keep a reasonable nu ber of layers 
per gyroradius. 
3. Calculation of Trans ort Coefficients in Energ S ace. First and 
second order coefficients DT and OTT were calculated in energy space 
by t  iff rent techniques. ne is ase   t e nstruction f a 
t ady tate istribution  i jecting articles ith  i gle ergy 
o (  e  i  t is case) a  re ing t e  e  t ey reach a  f t e 
t o preset boundaries "above" and "below" the injection point (see 
Moussas t I,  f r etails). 
nother ethod is based upon the ti e evolution of the energy 
istribution. ° is lculated ia  ast are it  cesive 
istributions Trst der  s. i e. f  ke  i fusion 
uation i  ergy, integrate for injection t o, ss e  irst 
order Taylor expansion in energy for OTT' and make a determination of 
the spread « "<T»2> e arrive at 
from where OTT can be calculated. 
th thods re neralizations f t ose initially eloped 
by J es t al ( ) t  st dy itch a gle s attering  a ra omly 
enerated I . 
e fect f t e ck is traced  unting ery article 
e counter ith it a  recording t e r sulting e ergy c ange. e 
average energy change is given by the ratio f the t tal gain and the 
er f s ck e counters. ransport efficients ca  e lculated 
sing t e time a  a erage article takes t  et ack t  t e s ck 
tB = 2A/V here A  me~n free path  0.03 AU (see aldes .. Galicia et aI, 
1~     arti l  el city. 
. c  haracteristics. e s c  se  in t i  st  ss  
through elios 2 on day 92 of 1976 hen the spacecraft as at 0.45 AU 
from the Sun. It is a perpendicular shock eB~ = 89° (Lepping et aI, 
1971) with a high Alfven Mach number MA = 7.5. The magnetic field 
ers oot i    as hi  is r   f t  nstr  
. 
It as assu e  t  e a la e s c  a  t  ere transfor ed 
t  a fra e here the Y~l plane c i ci es ith t at f the shock so 
that it is parallel to our layer planes. 
164 SH-1.5.1.
5. Results and Discussion. In figure I we present a resu]t of a time
stationary distribution of particles for an experiment carried out
using data from day 90/Helios I. It can be easily appreciated the
asymetry of the distribution towards the _right _j of the injection
energy To showing strong acceleration by waves. Boundaries were put
at + 2 tleV from To = I00 MeV. It should be noted that the mean free
path these partic]es is very smal] (k = 0.006 AU, Vald_s-Galicia et al,
1984).
Figure 2 shows an evolution diagram of the distribution
function of particles in energy and time. Contours are drawn for
different density levels. Areas with zero density within the distri-
bution are shown black. Injection energy is at the middle of the
figure and energy increases downwards. Full extension from top to
bottom is 6 MeV. The horizontal scale covers 2000 sec. Balck diamonds
represent first order momenta of particle distributions every 100 secs.
In table I we show the main results of this work. Transport
coefficients are average values of the calculations done by the two
different methods. Although not shown individually both values agree
within 15%. The second row of table I shows results for all particles
(85) used with Helios 2 day 92 sample including 79 shock crossings so
they are representative of the two proccesses involved (shock and
statistical acceleration),
We can aprecciate that even though average energy changes
corresponding to statistical and statistical plus shock acceleration
are greater than the shock produced average, transport coefficients
for this process are greater by an order of magnitude, In the last
column of the table we have calculated the the e-folding times (T)
corresponding to every experiment (Wibberenz et al, 1972). If we
calculate the time for adiabatic deceleration at 0,45 asuming
Vsw = 400 Km/sec and radial expansion we get _ad = 35.3 hours, Thus
altough statistical acceleration can have an effect in reducing the
adiabatic cooling only the shock accelerated particles are able to
overcome it at these energies,
Unfortunately we were limited by the time resolution of the
data and could not explore lower energies in a simi]ar manner,
6. Conclusions,
a) The time evolution and time stationary methods to calculate
transport coefficients agree quite well,
b) Statistical acceleration at particle energies of 100 MeV in the
inner Heliosphere is not able to overcome the effects of
adiabatic cooling.
c) Shock acceleration as opposed to statistical acceleration may be
a source of particles at these places an energies,
164 SH-l .5.1 • 
5. Results and Discussion. In figure 1 we present a result of a time 
stationary distribution of particles for an experiment carried out 
using data from day 90/Hel ios 1. It can be easi ly appreciated the 
asymetry of the distribution towards the "right" of the injection 
nergy To showing strong acceleration by waves. Boundaries were put 
at + 2 t1eV from To = 100 MeV. It should be noted that the mean free 
path these part icles is very small (A = 0.006 AU, Valdes-Gal icia et aI, 
1984). 
Figure 2 shows an evolution diagram of the distribution 
function of particles in nergy and time. C ntours are drawn for 
different density levels. Areas with zero density within the distri-
bution are shown black. Injection energy is at the middle of the 
figure and energy increases do nwards. Full extension from top to 
bottom is 6 MeV. The horizontal scale covers 2000 sec. Balck diamonds 
r present first order omenta of particle distributions every 100 secs. 
In table I we show the main results of this work. TranSDort 
coefficients are average values of the calculations done by the two 
different methods. Although not shown individually both values agree 
within 15%, The second row of table I shows re ults for all particles 
(85) used With Helios 2 day 92 sample including 79 shock crossings so 
they are representative of the two proccesses involved (shock and 
statistical acceleration), 
We can aprecciate that even though average energy changes 
corresponding to statistical and statistical plus shock acceleration 
are greater than the shock produced average, transport coefficients 
for this process are gr ater by an order of magnitude, In the last 
column of the table we have alculated the the e-folding times (T) 
corresponding to every experiment (\.Jibberenz et aI, 1972). If we 
calculate the time for adiabatic deceleration at 0.45 asuming 
V = 400 Km/sec and radial expansion we get T d = 35.3 hours. Thus 
sw a 
altough statistical acceleration can have an ffect in reducing the 
adiabatic cooling only the shock accelerated particles are able to 
overcome it at these energies. 
Unfortunately we were I imited by the time resolution of the 
data and could not explore lower n rgies in a similar manner, 
6. Conclusions, 
a) The time evolution and time stationary methods to calculate 
transport coefficients agree quite well. 
b) Statistical acceleration at particle nergies of 100 MeV in the 
inner Heliosphere is not able to overcome the effects of 
adiabatic cool in9' 
c) Shock acceleration as opposed to statistical acceleration may be 
a source of particles a  these places an n rgies. 
165 SH.-1,5,1
FIG I FIG 2
TABLEI
BOYISC POSITi0:I ACCELERATI0;I-AT> DT DTT T
(AU) PF%ESS (t'EV) (_EVS-1) (r:EVS-2) (HRS)
9ClHEL1 0.31 STATI:TICAL 0.76 (3.6_2.1)x10-4 (4z3)x10-4 76.5
92/HEL2 0.45 SHOCK.SIATISTIC_L0,83 (5,2Z2)xlO"4 (5_3,5)x10-4 53.
92/HEL2 0.43 SHOCK %20 (3,4±1,5)x10"3 (1Z,9)xlO-4 10,9
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5 H .. t. 5.1 
d) Statistical acceleration may be a more efficient process at 
lower energies. 
p ..... to lotH I 
(,\/1". 
J I 
'"Ic/ ~ 
h T ' ... v) _ I~ 
,-". 
,or t TOTAl. 'LIGHT 1' ... ,. at ,0) " .. 
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ABLE  
LOY/SC POSITiO:l ACCELr:R.mO;1 'llr> r 
( U) pr'JCES  Cf'c: ) (i'1 VS-1) 
9C/HEL. 1 0.31 ::TA T! :TI CAL .76 (3.6:t2.1.)Xl0-4 
921rlEL 2 0.45 SHOC~TS1~TISTIC4L 0.83 (5.2:t2)XI0-4 
92/HEL 2 0.45 SHOCI( 'l. E (3.4!1.5)XIO-3 
~~ENC1..~ 
AXFORD J. (l98H PROC XV II I. CR. C., 12, 155 
 .  . 976) HYS. J. E  ,  
  . 1  . I , L . 
lEP ING  .  . . " , 349. 
c.  .  . (1 ) lROPHYS. . T., QJ,  . 
~!OUS A~  I  982  . . l. 1 1 . 
Ll  .  . I. EV" , . --
  
n 
(t:E'tS-2) 
(4!3)Xl0-4 
(5!3.5)XIO-4 
U:!:.9)XIO-4 
I :I'RDSO  1.(984  . P.- CI., ,  
 ~1  984) . N  P. ~l R. 1"00" :ORIOKA,  I . 
L ES-GALIcI   .   , ,  
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~     N I   I  E   I )  
T 
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Shock and statistical acceleration of energetic particles in the interplanetary medium

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