Data were examined from two experiments aboard the Explorer 50 (IMP 8) spacecraft. The Johns Hopkins University/Applied Lab Charged Particle Measurement Experiment (CPME) provides 10.12 second resolution ion and electron count rates as well as 5.5 minute or longer averages of the same, with data sampled in the ecliptic plane. The high time resolution of the data allows for an explicit, point by point, merging of the magnetic field and particle data and thus a close examination of the pre- and post-shock conditions and particle fluxes associated with large angle oblique shocks in the interplanetary field. A computer simulation has been developed wherein sample particle trajectories, taken from observed fluxes, are allowed to interact with a planar shock either forward or backward in time. One event, the 1974 Day 312 shock, is examined in detail

Armstrong, T. P.

Bandle, J.

Kessel, R. L.

Nuber, R.

English

NASA Technical Reports Server

174
SHI.5-5
PARTICLE ACCELERATION DUE TO SHOCKS
IN THE INTERPLANETARY FIELD:
HIGH TIME RESOLUTION DATA AND SIMULATION RESULTS.
R.L. Kessel, T.P. Armstrong, R. Nuber, J. Bandle
Universlty of Kansas, Lawrence, KS, 66045, U.S.A.
INTRODUCTION
In thls study, data is examlned from two experiments
aboard the Explorer 50 (IMP 8) spacecraft. The Johns
Hopkins Unlverslty/Applied Physics Lab Charged Particle
Measurement Experlment (CPME) provides 10.12 second
resolution ion and electron count rates as well as 5.5
minute or longer averages of the same, wlth data sampled in
the ecllptlc plane. The Goddard Space Flight Center
Magnetic Field Experlment provldes the hlgh time resolution
magnetlc fleld data (15.36 sec). IMP 8 spends about half
its nearly clrcular (32 to 38 Re) orbit in the
interplanetary fleld. The high time resolution of the data
allows for an expllclt, polnt by polnt, merging of the
magnetic fleld and partlcle data and thus a close
examination of the pre- and post-shock conditions and
partlcle fluxes associated wlth large angle obllque shocks
in the Interplanetary fleld. A computer simulation has been
developed whereln sample particle trajectories, taken from
observed fluxes, are allowed to interact with a planar shock
elther forward or backward in time. Shock normals are
determlned from the single spacecraft method of Lepping and
Argentlero (i) uslng the Imp 8 magnetlc fleld data and OMNI
plasma data (J.W. King, NSSDC). One event, the 1974 Day
312 shock, is examined in detail.
DETERMINATION OF THE SHOCK NORMAL
The method of Lepplng and Argentlero is based on the
coplanarlty theorem (2) in whlch the normal is determined by
the magnetlc flelds:
!/-"+ "-_
"=
Instead of uslng the average values calculated from the
data, "best estimate" values are determlned In a manner to
be explalned below. Two assumptlons are necessary to use
thls method: flrst, that the Rankine-Hugoniot equations are
valid for interplanetary shocks; second, that the shock is a
step-function increase in all parameters, with superimposed
noise. Figure 1 lends credib111ty to the second assumption.
The flrst assumptlon is necessary because certaln of the
1  
TICLE ELERATION  TO S KS 
IN T  IN LANETARY F : 
SH 1.5-5 
  LUTION   IM LATION LTS. 
. . essel, . . r strong, . uber, J. andle 
niverslty f ansas, rence, , 6 45, . . . 
IN DUCTION 
In thlS study, data lS exa lned from two experiments 
aboard the xplorer 50 (IMP 8) s acecraft. The Johns 
opkins nlverslty/Applied ysics ab harged article 
easurement xperlment (CP E) r vides . 2 sec nd 
olution l   l ctron unt t s  ell  .  
inute or longer averages of the same, lth data sa pled in 
the ecllptlc plane. The oddard space light enter 
agnetic l ld perlment r vldes t e l h ti e r s lution 
agnetlc flel  data (15.36 sec). I P 8 spends about alf 
it  arly Clrcular (  t   e) rbit i  t  
i t rplanetary fl l . he i h ti e r s lution f t  ta 
allo s for an expllclt, pOlnt by pOlnt, erging of the 
agnetic l   artlcle ta  s  l se 
e amination f t e re- and st-shock nditions a d 
partlcle fluxes associated lth large angle obllque shocks 
i  t e l terplanetary fl ld.  co puter si ulation has been 
developed hereln sa ple article trajectories, taken fro  
observed fluxes, are allo ed to interact ith a planar shock 
lt er ard r ckward  e. hock rmals r  
determlned from the single spacecraft method of Lepping and 
rgentlero (1) uSlng the I p 8 agnetlc fleld data and O NI 
plasma data (J.W. Klng, NSSDC). One event, the 1974 Day 
2 ock,  amined l  etail. 
ETERMINATION F E CK ORMAL 
he ethod f e plny a d rgentlero lS ased  t e 
coplanarlty theorem (2) ln WhlCh the normal lS determined by 
e agnetlc l lds: 
I stead f USlng t e average alues alculated fr  t e 
ata, "best sti ate" alues re etermlned l  a anner t  
be explalned below. Two assumptlons are necessary to use 
thlS ethod: flrst, that the Rankine-Hugoniot equations are 
valid for i terplanetary shocks; second, at t e s ock  a 
step-function lncrease ln all parameters, with superimposed 
noise. Flgure 1 lends crediblllty to the second assumption. 
The flrst assumptlon is necessary because certaln of the 
https://ntrs.nasa.gov/search.jsp?R=19850026461 2020-03-20T17:02:28+00:00Z
175
SH I.5-5
Ranklne-Hugoniot equations are used as a constraint on the
shock normal. The equatlons in the shock rest frame are:
[pv.l= o
[B.I = o
Eleven varlables can be identlfled from these equations:
Three of these varlables ,s. , ..... , ....... ,
are isolated in terms of
the °ther eight" In the _'° _ __i'"'
Lepplng and Argentlero & s_ __
study any three varlables _ . __ _
could be isolated. Their oo I
data conslsted of 30 sec "_s
averaged magnetic field I-s0
_I_I
data and approximately 90 -7_
sec averaged plasma data. 0r: : : : : : : : ....... ,.
In thls study 15 sec _ _ ,[
averaged magnetlc field _ 0data was used along wlth 5 , "_ OZl_J
min averaged plasma data. -1o ItJilJ| itlill
Because of the large " 13 34 t_
standard devlatlons ,i;4d,_in_,i_¢_,id
associated wlth the solar :..-.,..._. ........ ,,-,,, .................. . ........... • ................. J-J_-31-_
wlnd data (wx,wy,Wz), .us_
partly due to the low _ _,
resolution of the data, it
w s necessary to isolate "_
these three varlables. To _""""'i.,._'....................." .............................
use them in the _ 45!_ m_
Ranklne-Hugonlot equatlons _ 0_,i' Ito solve for the other -4s_
varlables produced i___'-,'"","-',-,,_'.,"J-_-_-J'_
inconsistent results or no _iJ, f
convergence. _ 0_The m thod uses the -s
eight "known" varlables -3eo._...................................................3 _ 7 g u'*'"_nI_ 17 n n
and the three var tables .. J,_n2,of,,.,_
calculated from the _,_, o) ._._t,_ ,,.*_,.so_, _,_._ coo,_.oo,..
Vertical lines separaste [_e_d into pie- and post- shock
Rankine-Hugonlot °quations ,e_,o...h*c_.,,.s,_*.th,shock.o,,_*_,_,,,_._t_o.
b| S01a_ wlad _n 001°[ °€_p_c coord_nat_o Shock o_cu[s
In a type of least squares ,t,,0ho,,,
fit which IS m_n_mized by
use of an _terat_on process. The solution should converge
to the "best estimate" values relatlvely quickly. Many
starting values should be used and these compared to assure
convergence to the same mln_mum.
175 
S  1. 5-  
Rank1ne-Hugoniot equations are used as a constraint on the 
shock normal. The equat10ns 1n the shock rest fra e are: 
[pVnJ~  0 
[,Vn V, - B::{ = 0 
[YnBe - VeBnJ~ = 0 
[ nJ! = 0 
leven ar1ables an be 1dent1f1ed  t ese quations: 
hr  f t  ar1ables 
r   1  t s f 
the other eight. In the 
Lepp1ng and Argent1ero 
study any three var1ables 
could be isolated. Their 
ata ns1sted f  c 
averaged magnetic field 
data and approxi ately 90 
ec averaged plasma data. 
In th1S study 15 sec 
averaged magnet1c field 
data as used along 1th 5 
min averaged plas a data. 
Because of the large 
sta r  e 1at1 s 
associated w1th the solar 
w1nd data (Wx,Wy, z), 
partly due to the low 
res l ti  of the ata, it 
as necessary to 1solate 
these three var1ables. To 
use them 1n the 
Rank1ne-Hugon1ot equat10ns 
t  l e  t  t er 
var1ables produced 
incons1stent results or no 
convergence. 
e ethod s  
eight "known" var1ables 
 th  t e r1 les 
l l t  from the 
Rank1ne-Hugon1ot equat10ns 
1n a type of least squares 
fit hich 1S 1n1 ized by 
15 
i 10 
:. s 
.J S 
I 
.. 
·7 S 
14 
U74 ~.» 312 Mfj"nlt tlol~ 
i 
'90 
'1I0~~~~~~iIIIIIw~~~IIIdw&~~I&wdI"""":'~  , II Il IS 17 II 21 n 
1974 ~.» IU •• I.r WInd 
F1'J 1 iii' ""'lnetlc field 1n & lae eclq.ltlC co u.i.lndltu& 
. tlc"l 11ne. '.p c.atl h l  i to ,e- an  pOlt- .. oc  
re'llOnllt which Wf;I'l u&ed in the ,hock noraal deter.inAtion 
b) Sol , win  1n lola, Icllpt,c co dlnatel Shoc  oc r. 
.t 14 ]0 houCl 
use of an 1terat1on process. The Solut1on should converge 
to the " st estim te" lu s relat1v ly U1ckl . any 
start1ng values should be used and these co pared to assure 
convergence to the same m1n1mum. 
176
SH 1.5-5
This normal determination method was tested in several
ways. Multlple runs were made with different starting
values (partlcularly, dlfferent numbers of plasma points
were used from 15 min to 40 min of data), and these were
checked against each other. Three events were used; one,
the 1974 day 312 shock to be used in the remainder of thls
work, and two others which were checked agalnst thetabn
angles supplied by Tsurutanl (private comm.)--thetabn being
the angle between the magnetlc fleld and the shock normal.
The 1979 day 93 thetabn was calculated at 39 ° whlch is
within 4° of that calculated by Tsurutanl, and the 1979 day
95 thetabn Is wlthln 6 ° of the Tsurutanl value. The 1974
day 312 shock was not inclu,ded in the Tsurutani study. It ,_
was further checked by calculating the time of propagation
of the shock from the spacecraft along the shock normal to
the Earth and comparing against the reported SSC time. For
a calculated thetabn of 60 ° and a shock speed of 470 km/sec,
the time of arrival at Earth was 14.29 hours compared to the
reported 14.23 hours.
DESCRIPTION OF THE COMPUTER SIMULATION
The computer simulation is a further development of the
work of Chen (3). The frame of reference is as follows. A
plane shock is assumed movlng in the dlrectlon of the shock
normal (x directlon). The magnetic fleld is in the x-z
plane (By=0 upstream forces By=0 downstream). The upstream
plasma moves _n the -x direction, the downstream plasma in
the x-z plane. The electrlc fleld _s in the y direction and
constant across the shock. Data for a particular shock can
be made to flt these conditions by suitable rotations and
galilean transformations. The best estlmate values from the
prevlous section provide a conslstent set for this work
since they obey the Ranklne-Hugonlot equations (as they must
slnce they were determined from these equations). With thls
framework established, indivldual particles are allowed to
spiral in along magnetic field llnes and be reflected
upstream or transmltted downstream due to the change in
magnetic field at the shock surface and the Initial
conditlons. The particles move according to the Lorentz
force; each tlme a partlcle crosses the shock the flnal
conditions at the crossing point become the new initial
conditions, a,d the appropriate magnetic fleld Is inserted
into the force equatlon. The gain or loss in energy Is
monitored, along with the number of tlmes the particle
crosses the shock before being reflected or transmitted.
Particles can be inserted elther upstream or downstream from
the shock and can move either forward or backward in time.
DISCUSSION
Figure 2 shows the CPME data used _n the study. This is
the 290 keY to 500 keV sectored proton data. It is hlghly
structured on a short time scale partlcularly in the post
shock region. Associated wlth each of the "eight data
channels is a directlon consistent with the midpoint in the
8 
   
his r al termination ethod as t d  eral 
ays. ult1ple r s ere ade ith ifferent st rting 
lues ( art1cularly, 1fferent nu bers f las a ints 
ere d ro   i    in  ta),  se ere 
ecked ainst h t er. hr e ents ere ed; e, 
t  4   s ck t   d 1  t  r ainder f th1S 
ork, a  t  t ers hich ere ecked a1nst t t bn 
gles pplied  surutan1 ( rivate m.)--thetabn i g 
t  gle et een t  agnet1c f1 ld a  t  s ck r al. 
he 79   t t bn as lculated t ° Wh1Ch i  
ithin ° f t at lculated  surutan1, a  t  9 a  
 t bn 1S 1th1n  f  surutan1 alue. e 4 
y  s ck as t i l , d i  t  surutani st y. t 
as f rther ecked  lculating t  ti e f r pagation 
f t e shock fro  t e s acecraft al g t e shock nor al t  
t  arth  paring ainst t  orted  ti e. r 
 lculated t t bn f °   s ck ed f  /sec, 
t  ti e f rrival t arth as . 9 urs c pared t  t  
orted . 3 urs. 
ESCRIPTION   PUTER LATION 
e puter si ulation i  a f rt er el ent f t  
or  f hen ).  a e f ce 1S  s.  
l e s c  i  ass ed ov1ng i  t  lr tl n f t  s c  
nor al (x irect10n). he agnetic f1el  1S i  t e -z 
la e ( y O strea  f rces y=O nstream). he strea  
las a oves 1n t e -  ir ctl n, t e do nstrea  las a 1n 
t  -  l e. he l tr1c f1 l  15 1  t   ir ction  
nstant r ss t  s ck. ata f r a articular s ck  
be ade t  f1t t ese c nditi ns by s it le r t ti s and 
alil an t f r ations.  st t1 ate l es fro  t  
r 10us ti n r vide  nslstent t f r t i  or  
since they obey the ank1ne-Hugonlot equations (as they ust 
Sl e t  ere t r ined fro  t  uations). wit  th1S 
fra e ork t blished, 1 i 1dual rticles r  llo ed t  
s iral i  al  agnetic fi l  ll s and be r fl ted 
str  r t a 1tted nstream  t  t  ge 1  
agnetic i l  t t   e  t  1 itial 
ndit10ns. e articles ove ording t  t  orentz 
f r e; each t1 e a art1cle r sses t  s ck t  fl l 
c nditions t t e cr ssi g oint beco e t e ne  i iti l 
ndi tions, n.  t  propriate agnetic £l l  1S i rt d 
i t  t  f r  uatlon. he ai  r l  i  r y 1S 
onitored, al g it  t  nu ber f t1 es t  article 
r sses t  s ck f re i  r fl ted r tr s itted. 
articles can be i s rt d lt er strea  r do nstream fro  
 ck   ove i er ard  ard 1  e. 
I  
i ure 2 shows t e P E ata sed 1n t e st dy. his is 
the 290 kev t  500 kev sectored proton ata. It is h1ghly 
str ctured on a s ort ti e scale artlcularly i . the ost 
s ock r ion. sociated 1th ch f t  ei t ata 
a nels i   irectlon nsistent ith t  idpoint i  t e 
177
SH i,5-5
ecliptic plane of the 45 degree sampling angle. Plasma flow
collected for each of these channels will be in the opposite
direction. Magnetic field data is also available on this
high resolution time scale. For several of the peaks the
magnetic field is identified, and associated pltch angles
are determined for each of the elght channels. Then, using
a linear distribution of phase angles for each pitch, an
ensemble of partlcles is sent backward in time to the shock
surface.
The objectlve of thls study is a quantitatlve
determinatlon of the particle kinematics in the vicinity of
interplanetary shocks, in
particular the 1974 day .... ,,..... ,,', .., ....
312 shock. The .loooo; .it,
anisotropy of the _ .._,_ .J _ 11{ 11c_I
particle data at certain _ s_
peaMs together with the o :::::::::::::::::::::::phase averaged energy
changes, and comparisons, =lo_o i_
will be presented. _ i_0
lect_ 2
ACKNOWLEDGEMENTS 0 ..... ' ..... i ..... , .....1,,,,_,,,,, ,,,,, ,,,,v
The authors wlsh to t_ l_ i , I
i lictor )thank Dr. P. R. Brlggs 5_
for helpful suggestions
and technical assistance, o ''__.',_::,.,, ::::,_'', :
This work was supported _I_
||ct0r4in part by the NSF _ 5_through grant
ATM-7925987. o' ,,,.....,'....., ' ,.....,,, '' I_:_,
,,,M ,,
REFERENCES
i. R.P. Lepping and P.D. _ _
Argentlero, "Single Space- 0 :::::':':::':::::' IIII
craft Method of Estimating '_ '_[.''_'' ''''
Shock Normals", J. Geophys_ j_ Ilc%or 6
Res., 76,19, 1971. _ _
2. D.C. Colburn and C.P.
scont_nultles _Sonett, "D_ =
in the Solar Wind", Space _ ,,c.,,Sci. Rev., 5,439, 1966. _
3. G. Chin, "Numerlcal o :: : :: :: :: : :: :: :: ::: :: ::'' ' '' '' ' '[ '' '' ''I
Simulation of the Inter- _J_ il_ ,11 l I I
action of Charged Part- _ _
|ect_ |
icles with Obllque Mag-
netohydrodynamlc Shocks" %...... ' ..... '..... ' ......' ) 14 I_ It 17
PhD Thesis,Unlverslty Ig74d_317llCtMCo_trltli
of Kansas, 1975. ,,g2 6.actor,_.t,..€**pt_c_..°of 290_.vto
500 key p_oton data from the JHU/APL ¢hsrgod part*c1°
Rasaucl_aot Isper_len_ (CPNI) Shock occurs at 14 30 hrs
177 
SH 1.5-5 
ecliptic plane of the 45 degree sampling angle. Plasma flow 
collected for each of these channels will be in the opposite 
direction. Magnetic field data is also availabl  on this 
high resolution time scale. For several of the p aks t e 
magnetic field 1S 1dentified, and associated p1tch angles 
are determined for each of the e1ght channels. Then, using 
a linear distribution of phase angles for each pitch, an 
ensemble of part1cles is sent backward in time to the shock 
surface. 
The object1ve of th1S 
determinat10n of the particle 
interplanetary shocks, in 
particular the 1974 day 
st~dy 1S a quantitat1ve 
kinematics in the vicin y of 
312 shock. The :10000 
isotropy of the u= 
particle data at certain 5~ 
peaks together with the 
phase av raged energy 
changes, and comparisons, .10000 
will be presented. i u 5~ 
ACKNOWLEDGEMENTS 
The authors w1sh to .10000 
thank Dr. P. R. Bnggs I 5~ 
for helpful suggestions 
and technical assistance. 
This work was supported 
in part by the NSF 
through grant 
ATM-7925987. 
EF E CES • 10000 i 
1. R.P. Lepping and P.O. 
u 
A r g e n t 1 e r 0 , " S 1 n g 1 e Spa c e - OI-+-t-lI-++-t-+rt-+-HI-++-t-+-+-+-t-lI-++-t-H 
craft Method of Estimating 10000 
Shock Normals", J. Geophys~ 
Re s ., 76,19, 1971. 8 
2. D.C. Colburn and C.P. 
Sonett, "D~scont1nultles 
in the Solar Wind", Space 
Sci. Rev., 5,439, 1966. 
3. G. Chen, "Numer1cal 
Simulation of the Inter-
action of Charged Part-
icles with Obl1que Mag-
netohydrodynam1c Shocks", 
PhD Thesis, Un1vers1ty 
of Kansas, 1975. 
5~ 
rig l • IOctoCl In tho ocllptlc phn. of 290 koV to 
IIC\or 1 
,"C\or 7 
Ilctor ) 
•• ctor 4 
•• c\or • 
IIC\O' 1 
~OO keV p,oton diU frO. thl JHU/APL Ch .. god "'\lclo 
No"uro.ont a.pori.ont (C'NII Shock occurs .t 14 )0 hu 


Particle acceleration due to shocks in the interplanetary field: High time resolution data and simulation results

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