PH YS I CAL R EVI EW VOLUM E 75, NUMBER 8 APRIL 1S, 1949

On the Origin of the Cosmic Radiation

ENRICO FERMI
Institute for Nuclear Studies, University of Chicago, Ckicago, ILlinois
{Received January 3, 1949)

A theory of the origin of cosmic radiation is proposed according to which cosmic rays are originated
and accelerated primarily in the interstellar space of the galaxy by collisions against moving mag-
metic 6elds. One of the features of the theory is that it yields naturally an inverse power law for the
spectral distribution of the cosmic rays. The chief difhculty is that it fails to explain in a straight-
forward way the heavy nuclei observed in the primary radiation.

I. INTRODUCTION where H is the intensity of the magnetic field and

N recent discussions on the origin of the cosmic p is the density of the interstellar matter.
radiation E. Teller' has advocated the view One finds according to the present theory that a
that cosmic rays are of solar origin and are kept particle that is projected into the interstellar
relatively near the sun by the action of magnetic medium with energy above a certain injection
fields. These views are amplified by Alfvhn, Richt- threshold gains energy by coll'isions against the
myer, and Teller. ' The argument against the con- moving irregularities of the interstellar magnetic
ventional view that cosmic radiation may extend field. The rate of gain is very slow but appears
at least to all the galactic space is the very large capable of building up the energy to the maximum
amount of energy that should be present in form of values observed. Indeed one finds quite naturally
cosmic radiation if it were to extend to such a huge an inverse power law for the energy spectrum of the
space. Indeed, if this were the case, the mechanism protons. The experimentally observed exponent of
of acceleration of the cosmic radiation should be this law appears to be well within the range of the
extremely efficient. possibilities.
I propose in the present note to discuss a hy- The present theory is incomplete because no
pothesis on the origin of cosmic rays which attempts satisfactory injection mechanism is proposed except
to meet in part this objection, and according to for protons which apparently can be regenerated at
which cosmic rays originate and are accelerated least in part in the collision processes of the cosmic
primarily in the interstellar space, although they radiation itself with the diffuse interstellar matter.
are assumed to be prevented by magnetic fields The most serious difficulty is in the injection
from leaving the boundaries of the galaxy. The process for the heavy nuclear component of the
main process of acceleration is due to the interaction radiation. For these particles the injection energy
of cosmic particles with wandering magnetic fields is very high and the injection mechanism must be
which, according to Alfvbn, occupy the interstellar correspondingly efficient.
spaces.
Such fields have a remarkably great stability II. THE MOTIONS OF THE INTERSTELLAR MEDIUM
because of their large dimensions (of the order of It is currently assumed that the interstellar space
magnitude of light years), and of the relatively high of the galaxy is occupied by matter at extremely
electrical conductivity of the interstellar space. low density, corresponding to about one atom of
Indeed, the conductivity is so high that one might hydrogen per cc, or to a density of about 10 "g/cc.
describe the magnetic lines of force as attached to The evidence indicates, however, that this matter
the matter and partaking in its streaming motions. is not uniformly spread, but that there are conden-
On the other hand, the magnetic field itself reacts sations where the density may be as much as ten
on the hydrodynamics' of the interstellar matter or a hundred times as large and which extend to
giving it properties which, according to Alfvkn, can average dimensions of the order of j.o parsec.
pictorially be described by saying that to each line (1 parsec. =3.1)&10'8 em=3. 3 light years. ) From
of force one should attach a material density due to the measurements of Adams4 on the Doppler effect
the mass of the matter to which the line of force is of the interstellar absorption lines one knows the
linked. Developing this point of view, Alfthn is radial velocity with respect to the sun of a sample
able to calculate a simple formula for the velocity of such clouds located at not too great distance from
V of propagation of magneto-elastic waves: us. The root mean square of the radial velocity,
V = H/(4s p) &, (1) corrected for the proper motion of the sun with
' Nuclear Physics Conference, Birmingham, 1948. respect to the neighboring stars, is about 15 km/sec.
~Alfvdn, Richtmyer, and Teller, Phys. Rev. , to be pub- We may assume that the root-mean-square velocity
lished.
I H. Alfv4n, Arkiv Mat, f. Astr. , o. Fys. 298, 2 (1943). 4 W. S. Adams, A.
p. J. 9'7, 105 (1943).
ii69
 E N R I CO FERM I

is obtained by multiplying this figure by the square III. ACCELERATION OF THE COSMIC RAYS
root of 3, and is therefore about 26 km/sec. Such We now consider a fast particle moving among
relatively dense clouds occupy approximately 5 such wandering magnetic 6elds. If the particle is
percent of the interstellar space. ' a proton having a few Bev energy, it will spiral
Much less is known of the much more dilute around the lines of force with a radius of the order
matter between such clouds. For the sake of of 10" cm until it "collides" against an irregularity
definiteness in what follows, the assumption will be in the cosmic 6eld and so is reflected, undergoing
made that this matter has a density of the order of some kind of irregular motion. On a collision both
10 ", or about 0. 1 hydrogen atoms per cc. Even a gain or a loss of energy may take place. Gain of
fairly extensive variations on this figure would not
energy, however, wi11 be more probable than loss.
very drastically alter the qualitative conclusions. This can be understood most easily by observing
If the assumption is made that most of this material that ultimately statistical equilibrium should be
consists of hydrogen atoms, it is to be expected that established between the degrees of freedom of the
most of the hydrogen will be ionized by the photo- wandering fields and the degrees of freedom of the
electric effect of the stellar light. Indeed, one can particle. Equipartition evidently corresponds to an
estimate that some kind of dissociation equilibrium unbelievably high energy. The essential limitation,
is established under average interstellar conditions,
therefore, is not the ceiling of energy that can be
outside the relatively dense clouds, for which attained, but rather the rate at which energy is
n+'/no = (Ti) &, acquired. A detailed discussion of this process of
acceleration will be given in Section VI. An ele-
where n+ and no are the concentrations of ions and mentary estimate can be obtained by picturing the
neutral atoms per cc, and T~ is the absolute kinetic "collisions" of the particles against the magnetic
temperature in degrees K. Putting in this formula irregularities as if they were collisions against
n+=0. 1, one 6nds that the fraction of undissociated reflecting obstacles of very large mass, moving
atoms is of the order of 1 percent, even assuming with disordered velocities averaging to V= 30
a rather low kinetic temperature of the order of km/sec. Assuming this picture, one finds easily
100'K. that the average gain in energy per collision is given
It is reasonable to assume that this very low as order of magnitude by
density medium mi11 have considerable streaming
motions, since it will be kept stirred by the moving Re = 8'm,
heavier clouds passing through it. In what follows,
a root-mean-square velocity of the order of 30 where m represents the energy of the particle
km/ ec. will be assumed. According to Alfvhn's inclusive of rest energy, and 8= U/c=10 '. This
picture, we must assume that the kinetic energy of corresponds, therefore, for a proton to an average
these streams will be partially converted into mag- gain of 10 volts per collision in the non-relativistic
netic energy, that indeed, the magnetic field will region, and higher as the energy increases. It
build up to such a strength that the velocity of follows that except for losses the energy will increase
propagation of the magneto-elastic waves becomes by a factor e every 10' collisions. In particular, a
of the same order of magnitude as the velocity of particle starting with non-relativistic energy will
the streaming motions. From (1) it follows then attain, after N collisions, an energy
that the magnetic field in the dilute matter is of = Mc'
w exp (B'A').
the order of magnitude of 5 &10 6 gauss, while its
intensity is probably greater in the heavier clouds. Naturally, the energy can increase only if the losses
The lines of force of this field will form a very are less than the gain in energy. An estimate to be
crooked pattern, since they will be dragged in all given later (see Section VII) indicates that the
directions by the streaming motions of the matter ionization loss becomes smaller than the energy
to which they are attached. They will, on the other gain for protons having energy of about 200 Mev.
hand, tend to oppose motions where two portions For higher energy the ionization loss practically
of the intersteIIar matter try to Row into each becomes negligible. %e shall discuss later the
other, because this mould lead to a strengthening injection mechanism.
of the magnetic held and a considerable increase of
magnetic energy. Indeed, this magnetic eR'ect will IV. SPECTRUM OF THE COSMIC RADIATION
have the result to minimize what otherwise would
be extremely large friction losses which would damp During the process of acceleration a proton may
the streaming motions and reduce them to dis- lose most of its energy by a nuclear collision. This
ordered thermal motions in a relatively short time. process is observed as absorption of primary cosmic
radiation in the high atmosphere and occurs with
' B. Stromgrcn, A. p. J. 108, 242 (1948). a mean free path of the order of magnitude of 70
 OR I 6 I N OF COSM I C RA D I ATION

g/cm', corresponding to a cross section of about of the order of a light year, or about 10" cm. Such
a collision mean free path seems to be quite
o =25X10 "cm' (5) reasonable.
per nucleon. The theory explains quite naturally why no
In a collision of this type most of the kinetic electrons are found in the primary cosmic radiation.
energy of the colliding nucleons is probably con- This is due to the fact that at all energies the rate
verted into energy of a spray of several mesons. of loss of energy by an electron exceeds the gain.
It is reasonable to assume that the cosmic rays At low energies, up to about 300 Mev, the loss is
will occupy with approximately equal density all mainly due to ionization. Above this energy radi-
the interstellar space of the galaxy. They will be ative losses due to the acceleration of the electrons
exposed, therefore, to the collisions with matter of in the interstellar magnetic field play the dominant
an average density of 10 '4, leading to an absorption role. This last energy loss is instead quite negligible
mean free path for protons. Also, the inverse Compton e8ect
4=7&10" cm. (6) discussed by Feenberg and Primako6' will con-
A particle traveling with the velocity of light will tribute to eliminate high energy electrons.
traverse this distance in a time V. THE IN JECTION MECHANISM. DIFFICULTIES
T=ti/c=2X10" sec. VfITH THE INJECTION OF HEAVY NUCLEI

or about 60 million years. In order to complete the present theory, the

The cosmic-ray particles now present will there- injection mechanism should be discussed.
fore, in the average, have this age. Some of them In order to keep the cosmic radiation at the
will have accidentally escaped destruction and be present level it is necessary to inject a number of
considerably older. Indeed, the absorption process protons of at least 200 Mev, to compensate for
can be considered to proceed according to an those that are lost by the absorption process.
exponential law. If we assume that original particles According to recent evidence, ' the primary cosmic
at all times have been supplied at the same rate, radiation contains not only protons but also some
we expect the age distribution now to be relatively heavy nuclei. Their injection energy is
much higher than that of protons, primarily on
exp( —t/T) dt/T. (8) account of their large ionization loss. (See further
During its age t, the particle has been gaining
Section VII.) Such high energy protons and heavier
nuclei conceivably could be produced in the vicinity
energy. If we call v. the time between scattering
collisions, the energy acquired by a particle of age of some magnetically very active star. ' To state
t will be this, however, merely means to shift the difficulty
from the problem of accelerating the particles to
w(t) = Mc' exp(B't/r) (9) that of injecting them unless a more precise esti-
Combining this relationship between age and energy mate can be given for the efficiency of this or of
with the probability distribution of age given some equivalent mechanism. With respect to the
previously, one finds the probability distribution of injection of heavy nuclei I do not know a plausible
the energy. An elementary calculation shows that answer to this point.
the probability for a particle to have energy For the production of protons, however, one
between m and m+dm is given by might consider also a simple mechanism which, if
'r. (10) the present theory is at all correct in its general
s(w)dw=(7/B'T)(Mc')'s'rdw/w'+' features, should be responsible for at least a large
It is gratifying to find that the theory leads natu- fraction of the total number of protons injected.
rally to the conclusion that the spectrum of the According to this mechanism the cosmic radiation
cosmic radiation obeys an inverse power law. By regenerates itself as follows. When a fast cosmic-ray
comparison of the exponent of this law with the proton collides in the interstellar space against a
one known from cosmic-ray observations, that is, proton nearly at rest, a good share of the energy
about 2.9, one finds a relationship which permits wi11 be lost in the form of a spray of mesons, and
one to determine the interval of time v between two nucleons wi11 be left over with energy much
collisions. Precisely, one finds: 2.9 = 1+r/B'T, less than that of the original cosmic ray. Estimates
from which follows indicate that in some cases both particles may have
v = j..98'T. an energy left over above the injection threshold of
6 E. Feenberg and H. PrimakoE, Phys. Rev. 73, 449 (1948).
Using the previous values of 8
and T, one finds 'Freier, Lofgren, Ney, and Oppenheimer, Phys. Rev. 74,
v=4&10~=j..3 years. Since the particles travel 1818 (1948); H. L. Bradt and B. Peters, Phys. Rev. 74, 1828
with approximately the velocity of light, this (1948).
8See for examp1e W. F. G. Swann, Phys. Rev. 43, 217
corresponds to a mean distance between collisions (1933) and Horace %. Babcock, Phys. Rev. 74, 489 (1948).
 FERM I

200 Mev, in some cases one and in some cases none. But even if this stabilizing mechanism is not
We can introduce a reproduction factor k, defined adequate to keep the reproduction factor at the
as the average number of new protons above the value one, and therefore an appreciable change in
injection energy arising in a collision of an original the general level of the cosmic radiation occurs
cosmic-ray particle. As in a chain reaction, if k is over periods of hundreds of millions of years, the
greater than one the over-all number of cosmic rays general conclusions reached in Section IV would
will increase; if k is less than one it will decrease; not be qualitatively changed. Indeed, if k were
if k is equal to one it will stay level. somewhat different from one, the general level of
Apparently the reproduction factor under inter- the cosmic radiation would increase or decrease
stellar conditions is rather close to one. This is exponentially, depending on whether k is larger
perhaps not a chance, but may be due in part to than or less than one. Consequently the number of
the following self-stabilizing mechanism. The mo- cosmic particles injected according to the mecha-
tions of the interstellar matter are not quite con- nism that has been discussed will not be constant
servative, in spite of the reduced friction, caused by in time but will vary exponentially. Combining
the magnetic 6elds. One should assume, therefore, this exponential variation with the exponential
that some source is present which steadily delivers absorption (8), one still finds an exponential law
kinetic energy into the streaming motions of the for the age distribution of the cosmic particles at
interstellar matter. Probably such a source of the present time, the only difference being that the
energy ultimately involves conversion of energy period of this exponential will be changed by a
from the large supplies in the interior of the stars. small numerical factor.
The motions of the interstellar medium are in a The injection mechanism here proposed appears
dynamic equilibrium between the energy delivered to be quite straightforward for protons, but utterl&
by this source and the energy losses caused by inadequate to explain the abundance of the heavy.
friction and other causes. In this balance the nuclei in the primary cosmic radiation. The injec-
amount of energy transferred by the interstellar tion energy of these particles is of several Bev, and
medium to cosmic radiation is by no means ir- it is dif6cult to imagine a secondary effect of the
relevant, since the total cosmic ray energy is cosmic radiation on the diffuse interstellar matter
comparable to the kinetic energy of the streaming, which might produce this type of secondary with
irregular motions of the galaxy. One should expect, any appreciable probability. One might perhaps
therefore, that if the general level of the cosmic assume that the heavy particles originate at the
radiation should increase, the kinetic energy of the fringes of the galaxy where the density is probably
interstellar motion would decrease, and vice versa. lower and the injection energy is therefore probably
The reproduction factor depends upon the density. smaller. This, however, would require extreme
As the density increases, the ionization losses will conditions of density which are not easily justihable.
increase proportionally to it. This tends to increase It seems more probable that heavy particles are
the injection energy and consequently to decrease injected by a totally different mechanism, perhaps
the reproduction factor. On the other hand, also, as a consequence of the stellar magnetism.
the rate of energy gained will change by an amount If such a mechanism exists one mould naturally
which is hard to de6ne unambiguously. One might expect that it would inject protons together with
perhaps assume, however, that the velocity of the heavier nuclei. The protons and perhaps to a
wandering magnetic 6elds increases with the somewhat lesser extent the n-particles would be
power of the density, as would correspond to the further increased in numbers by the "chain reac-
virial theorem, and that the collision mean free tion" which in this case should have k &1. Indeed
path is inversely proportional to the -', power of the their number would be equal to the number injected
density, as one might get from geometrical simili- during the lifetime T increased by the factor
tude. One would 6nd that the rate of energy increase 1/(1 — k). Heavy particles instead would slowly
is proportional only to the -', power of the density. gain or slowly loose energy according to whether
The net effect is an increase of the injection energy their initial encl;gy is above or below the injection
and a decrease of the reproduction factor with threshold. They would, however, have a shorter
increasing density. If the reproduction factor had lifetime than protons because of the presumably
been initially somewhat larger than one, the general larger destruction cross section. Their number
level of the cosmic radiation would increase, drain- should be approximately equal to the number
ing energy out of the kinetic energy of the galaxy. injected during their lifetime.
This would determine a gravitational. contraction One should remark in this connection that a
which would increase the density and decrease k consequence of the present theory is that the energy
until the stable value of one is reached. The spectrum of the heavy nuclei of the cosmic radiation
opposite would take place if k initially had been should be quite different from the spectrum of the
considerably less than one. protons, since the absorption cross section for a
 ORIGIN OF COSMIC RADIATION j. i 73

heavy particle is presumably several times larger

than that of a proton. One would expect, therefore,
that the average age of a heavy particle is shorter =b
than the age of a proton, which leads to an energy FCear. um
spectrum decreasing much more rapidly with energy
for a heavy particle than it does for protons. An FiG. 1. Type 8 reHection of a cosmic-ray particle.
experimental check on this point should be possible.
VI. FURTHER DISCUSSION OF THE reflection). Here again, the energy of the particle
MAGNETIC ACCELERATION would not change if the magnetic held were static.
In this section the process of acceleration of the On the other hand, the lines of force partake of
cosmic-ray protons by collision against irregularities the streaming motions of the matter, and it may
of the magnetic field will be discussed in somewhat happen that the line of force at the bottom of the
more detail than has been done in Section III. curve moves in the direction indicated by the
The path of a fast proton in an irregular magnetic arrow a, or that it moves in the direction indicated
field of the type that we have assumed wi11 be by the arrow b. In the former case there will be
represented very closely by a spiraling motion an energy gain (head-on collision) while in case b
around a line of force. Since the radius of this (overtaking collision) there will be an energy loss.
spiral may be of the order of 10" cm, and the Gain and loss, however, do not average out com-
irregularities in the field have dimensions of the pletely, because also in this case a head-on collision
order of 10" cm, the cosmic ray will perform many is slightly more probable than an overtaking colli-
turns on its spiraling path before encountering an sion due to the greater relative velocity.
appreciably different 6eld intensity. One finds by The amount of energy gained or lost in a collision
an elementary discussion that as the particle of the two types described can be estimated with a
approaches a region where the 6eM intensity simple argument of special relativity, without any
increases, the pitch of the spiral will decrease. One reference to the detailed mechanism of the collision.
finds precisely that In the frame of reference in which the perturbation
of the 6eld against which the collision takes place
sin%/II = constant, (12) is at rest, there is no change of energy of the
where 8 is the angle between the direction of the particle. The change of energy in the rest frame of
line of force and the direction of the velocity of the reference is obtained, therefore, by 6rst transform-
particle, and H is the local field intensity. As the ing initial energy and momentum from the rest
particle approaches a region where the 6eld intensity frame to the frame of the moving perturbation. In
is larger, one will expect, therefore, that the angle this frame an elastic collision takes place whereby
8 increases until sin8 attains the maximum possible the momentum changes direction and the energy
value of one. At this point the particle is rejected remains unchanged. Transforming back to the
back along the same line of force and spirals back- frame of reference at rest, one obtains the final
wards until the next region of high field intensity is values of energy and momentum. This procedure
encountered. This process will be called a "Type A" applied to a head-on collision, gives the following
reAection. If the magnetic field were static, such a result,
reAection would not produce any change in the
kinetic energy of the particle. This is not so,
1+2BP cos6+8'
however, if the magnetic field is slowly variable. K' 1— B'
It may happen that a region of high field intensity
moves toward the cosmic-ray particle which collides where pc is the velocity of the particle, 0 is the
against it. In this case, the particle will gain energy angle of inclination of the spiral, and Bc is the
in the collision. Conversely, it may happen that velocity of the perturbation. It is assumed that the
the region of high field intensity moves away from collision is such as to produce a complete reversal
the particle. Since the particle is much faster, it of the spiraling direction by either of the two
will overtake the irregularity of the 6eld and be mechanisms outlined previously. For an overtaking
reAected backwards, in this case with loss of energy. collision, one finds a similar formula except that
The net result will be an average gain, primarily for the sign of 8 must be changed. We now average
the reason that head-on collisions are more frequent the results of head-on and overtaking collisions,

8/—
than overtaking collisions because the relative taking into account that the probabilities of these
velocity is larger in the former case. two types of events are proportional to the relative
Somewhat similar processes take place when the velocities and are given therefore by (P cos8+8/
cosmic-ray particle spirals around a curve of the 2P cosO) for a head-on collision and (P cos8
line of force as outlined in Fig. 1 ("Type 8" 2P cos8) for an overtaking collision, The result for
 E N R I CO FERM I

TABLE I. Energy loss per g/em~ of material traversed. Section III a value of 200 Mev for this "injection
energy" has been given; a justihcation for this
Energy Loss/g/cm~ Gain/g/cm~
assumed value wil. l be given now. In estimating
10' ev 94 X10' ev 7.8 X10' ev the injection energy we will assume that the
10' 15 Xio' 8.6X106
109 4.6X10' 16.1X106 particle, during its acceleration, 6nds itself both
101,0 4 6X 106 91 X 10' inside relatively dense clouds and in the more
dilute material outside of the douds for lengths of
time proportional to the volumes of these two
the average of ln(w'/w) up to terms of the order of regions. The ionization loss will be due, therefore,
8 is' to a material of an average density equal to the
(In(w'/w))A, ——4B' —28'P' cos'8 (14) average density of the interstellar matter, which
which confirms the order of magnitude for the has been assumed to be 10 " g/cm', consisting
average gain of energy adopted in Section III. mostly of hydrogen. In Table I the energy loss per
As a result of the extreme complication of the g/cm' of material traversed is given a,s a function
magnetic field and of its motion, it does not appear of the energy of the proton. In the third column of
practical to attempt an estimate by more than the the table the corresponding energy gain is given.
order of magnitude. It is seen that the loss exceeds the gain for particles
One might expect that after a relatively short of energy less than about 200 Mev, as has been
time the angle 0 will be reduced to a fairly low stated.
value so that Type A reflections will become A similar estimate yields for the acceleration of
infrequent. This is due to the fact that when 8 is n-particles an injection energy of about 1 Bev, for
large, fairly large increases in energy and decreases the acceleration of oxygen nuclei the initial energy
of 8 may occur, if the particle should be caught required is about 20 Bev, and for an iron nucleus
between two regions of high field moving against it would amount to about 300 Bev. As already
each other along a force line. One can prove that stated, it does not appear probable that the heavy
Type 8reRections change gradually and rather nuclei found in the cosmic radiation are accelerated
slowly the average pitch of the spiral. It appears, by the process here described, unless they should
therefore, that except for the beginning of the originate at some place in the galaxy where the
acceleration processes the Type A will not give as interstellar material is extremely dilute.
large a contribution as one otherwise might expect. I would like to acknowledge the help that I had
from several discussions with E. Teller on the
VII. ESTIMATE OF THE INJECTION ENERGY relative merits of the two opposing views that we
Acceleration of a cosmic-ray particle will not be are presenting. I learned many facts on cosmic
possible unless the energy gain is greater than the magnetism from a discussion with H. Alfvbn, on
ionization loss. Since this last is very large for the occasion of his recent visit to Chicago. The
protons of low velocity, only protons above a views that he expressed then were quite material
certain energy threshold will be accelerated. In in inAuencing my own ideas on the subject.