Download Radiation of Fast Charged Particles in Media?

CHIl’iESE JOURNAL OF PHYSICS
JUNE 1992
VOL. 30, NO. 3
Radiation of Fast Charged Particles in Media?
C. Yang
Depurttnent of Physics, Tutnkung University, Tumslli, Tuiwun 25137, R.O.C.
und
Yerevun Physics Instihite, Yerevun, 375036, Republic ofAmzeniu
(Received Febnmy 20,1992)
The theory of electromagnetic radiation generated by a fast charged particle passing at a
constant velocity through a uniform medium (the Vavilov-Cherenkov radiation), a non-uniform
medium (the transition radiation), or a single crystal (the quasi-Cherenkov radiation) is briefly
reviewed. Several main experimental results and the applications in constructing high-ener,v
particle detectors are discussed. The hard radiation emitted by charged particles moving in a
crystal at small angles relative to crystallographic axes and planes in the regime of channeling
or
quasichanneling and the influence of particles incoherent scattering are also discussed.
.
I. INTRODUCTION
It is well known that when the direction or the magnitude of the velocity of a charged particle changes bremstrahlung is generated. Moving at a constant velocity in vacuum a charged
particle does not generate electromagnetic radiation. In medium atoms emit secondary
electromagnetic waves under the influence of the passing charged particle. These secondary
waves mutually cancel out completely, if the medium is uniform and stable and the particle
velocity is less than the phase velocity of the electromagnetic wave in this medium. But while
either one of these mentioned conditions is not satisfied, the complete cancellation of the secondary waves emitted by the atoms is impossible, then a resultant electromagnetic radiation appears. This radiation appears even at constant particle velocity, * so it differs from bremstrahlung in principle. In a uniform medium this is the Vavilov-Cherenkov radiation’ (see also2J).
In nonuniform media, say, when a particle crosses the boundary between two different media,
the resultant radiation is called transition radiation4 (see also’). In a crystal, radiation of X-ray
frequencies is formed as a result of the microscopic nonuniformity due to the periodic arrangement of atoms and it is called the quasi-Cherenkov radiation 6 (see also’) .
In this paper the theory of Vavilov-Cherenkov radiation, transition radiation and quasiCherenkov radiation is briefly reviewed. Several main experimental results and the applications
‘Refereed version of the invited paper presented at the Annual Meeting of the Physical Society of R.O.C., Janualy24-25,
1992.
321
81992 THE PIHYSICAL S0CIEZ-Y
OF THE REPUBLIC OF CHINA
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RADIATION OF FAST CHARGED PARTICLES Ih’ MEDIA
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of the X-ray transition radiation in constructing high-energy particle detectors are discussed.
The so-called channeling radiation emitted by fast electrons or positrons moving in a
monocrystal at small angles relative to crystallographic axes and planes in the regime of channeling or quasichanneling is also discussed as well as the influence of particles incoherent scattering. This kind of bremstrahlung has many interesting features for possible applications.
II. TRANSITION RADIATION
Classical macroscopic electrodynamics may be used in treating the problems of radiation
formation by fast charged particles in amorphous media. If the wave length is much greater than
the atomic radius (which is true for visible light and radiowaves) the usage of classical
electrodynamics is doubtless. When the wave length is of the same order of the atomic radius
(for X-rays) or shorter (but the photon energy is not enough for particles creation), classical
electrodynamics is still allowable for use since the formation length (see § III) of the forward
propagating radiation is a macroscopic quantity. Besides, if the radiation energy is much smaller
than the particle energy, the particle motion may be regarded as classical and as unsubjected
to the influence of the radiation.
The Fourier amplitudes E(k, o) and H(k, w) (for simplicity we shall write E and H) of the
electric and magnetic fields E(r, t) and H(r, t) are described by Maxwell’s equations
ikxH=- ZWEE + Fj,(k,u),
C
ikxE= %!L!,,
c
pk.H=O,
(1)
i&k. E = 4ap,(k,w).
Here we suppose that the medium is uniform and its parameters do not change with time,
E = E(O) and ,u = ,LL(W) are its dielectric and magnetic susceptibilities, respectively, and j,(k,w)
and pe(k,o) are the Fourier amplitudes of external current and charge densities.
In the case when a particle with charge e moves at a constant velocity v along the z-axis
we have
.L(k,w) = vp,(k,u)
From (1) and (2) it is not difficult to derive
(2)
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C. YANG
E particle(k, u) = -& “k~~V~“:~P~,~z)U
H particle(k,W) = $k X Eparticle(k,W),
323
6(k, - :),
P = E,
(3)
(n, is a unit vector along the z-axis and kl is the projection of k onto the xy-plane).
Now we suppose that at z = 0 there is a plane interface of two media with different
dielectric and magnetic susceptibilities. It is easy to see that the electric and magnetic fields
Eparticle(rJ) and Hparticle (r,t) do not satisfy the boundary conditions: the tangential components
of the fields must be continuous at the boundary. To satisfy these boundary conditions we must
add to the particular solution (3) of the inhomogeneous Maxwell’s equations (1) certain solution
&ad and Hrad of the homogeneous Maxwell’s equations:
H = Hparticle + H rad .
E = Eparticle + Erad,
From the boundary conditions we can find out Erad and Hrad and then the radiation intensity. For example, in the case of medium-vacuum (E = E’ + i&” , p = 1 at z < 0 and E = ,U
= 1 at z > 0) we obtain for the intensity of forward propagating radiation
PI’(+) = /- dw /+ de
JO
JO
d?W(+)(w, 8)
~~
dwd0
where
2eyI& - l/‘/l -/3&Z& - p2i2
d2W(++, 0)
dwdb’
=
nc(l - p2 cosz 8)2/l - /3&ZS~?
sin3 e c0s2 e
(4
xI & cos e + &YEZ+
is the frequency-angular distribution of the radiation intensity.
II-l. Vavilov-Cherenkov peak
In a sufficientIy transparent medium (E” c < 1) which happens to satisfy the following
inequalities
there is a peak at the angle
9 vc = sin-l
d5’
1
_ p?
(6)
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RADIATIOh’ OF FAST CHARGED PARTICLES IN MEDIA
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for Eq. (4). The physical meaning of these two inequalities (5) is quite clear. The left one means
that the particle velocity is greater than the radiation phase velocity in the medium, i.e. VavilovCherenkov radiation (VCR) is formed in the medium. The second inequality means that the
formed VCR can go out from the medium to vacuum (without total reflection at the boundary).
Integrating (4) over 8 near &c we have
dW$ (w)
dw
=
I(w) labs+),
where I(W) is the intensity of VCR formed in unit length along the particle trajectory in the
medium’:
I(-,=+&),
(8)
labs is the absorption length of VCR:
.
C
I abs = pw &” ’
(9
and T(o) is the transmission coefficient of the radiation at the boundary:
4&l/3 cos 8vc
T(w) = (E’P cos 0°C + 1)‘.
(10)
It can be seen from (7)-(10) that VCR is determined only by particle velocity, but not
directly by the particle Lorentz-factor y. So for high-energy particles both the emission angle
and the intensity of VCR are practically independent of the particle energy.
11-2. ‘Transition radiation peak
The difference between Eq. (4) (which corresponds to the total radiation) and the VCR
peak is caused entirely by particle transition through the boundary, so this difference (or the
whole (4) if inequalities (5) are not satisfied) describes transition radiation (TR). It is not difficult to see that there is a sharp peak in TR formed by high-energy particles at a small angle
e--Y -l,
-I=
&pi,
and the peak value is proportional to y. If visible light or longer waves (OTR) are under consideration, the radiation intensity after integration over 0 is
d’W gR(w,
dwdO
0) _ 2 ,ny
c
.
(11)
--
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C. YANG
QL
02
43
0.4
0.5
325
06
0.7
0.8
09
/
0 (rad)
FIG. 1. Angular distribution of OTR intensity’at a given frequency: E’ = 1.6, E” = 0.01. Numbers near curves mean particle Lorentz-factor y.
.
Generally speaking, this quantity depends on E(W).
Distribution curves of OTR intensity calculated by Eq. (4) are represented in Fig. 1. The
peaks on the left side (0 < 0.05 rad) are TR peaks. Two peaks on the right side (0 = 0.545 and
0.875 rad) are VCR peaks. TR peaks appear only at y > > 1 and depend on ‘J. VCR peaks
are independent of y at y > > 1.
11-3. X-ray transition radiation
In the X-ray region (the photon energy is from several keV to several hundreds keV) IE
-11 <c 1:
W=
&=l--$+$&‘,
(12)
where wP is the plasma frequency of the medium (w > > wP). In this region conditions (5) cannot be satisfied, thus VCR cannot appear, whereas high-energy particles (y > > 1) form transition radiation of X-ray frequencies (XTR) propagating forward under small angles (0 < < 1).
In this case Eq. (4) may be written as
d2W$&(w, 8)
dwde
2e2
I& - 11283
= -G (74 + e=)=ly--= + 82 + 1 - El=.
(13)
It can be seen from (13) that angles which give the main contribution to XTR are
e 2 e,,,,
e,,, - 417-” + 1 - ~1~‘~.
Integrating (13) over 8 and ignoring E” (E’ ’ c < oP2/w’) we obtain
dW$&tW
dw
=~[(~+-$&)ln(l+~)-I].
(14
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RADIAGON OF FAST CHARGED PARTICLES IN MEDIA
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We see from it that for
w < wpy
(1%
intensities of XTR and OTR are of the same order and are approximately proportional to In w
and In y, whereas for
w > wpy
(16)
the intensity of XTR decreases rapidly as ~I.J~.
Integrating (14) over o we obtain the total intensity of XTR7
e7
(+)
j/t;, TR - ZWPY.
(17)
It is important to point out that the total intensity of XTR is proportional to the particle Lorentzfactor y.
When a particle moves from vacuum into medium the backward radiation has no VCR
peak and consists of only TR mainly in the optical region. The backward XTR is very weak.
III. CASES OF MANY BOUNDARIES
Transition radiation formed by one single boundary is not very strong and is of the order
of
1
fit = 137
e’
photons per particle. So for practical applications many boundaries should be used.
Passing through many boundaries a charged particle generates TR (including possible
VCR) at every single one of them. The observed radiation is the final result of interference.
Every secondary wave (see Introduction) emitted from a certain point of particle trajectory has
its own phase. If the phase difference is much smaller than x, secondary waves interfere constructively. Otherwise they cancel one another partly or completely. The distance for which the
phase difference isn is very important in treating radiation formation and is called the formation
length:
Z,ll =
rv
WI1 -
(18)
pv&osQ~’
If
I&-11<1,
_..._..
y)>l,
8<1
(19)
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321
(for X-ray region, high-energy particles and small radiation angles) Eq. (18) may be approximately written as
2irv
wly-2 + 0” + 1 - El.
z,Il x
(20)
So when inequalities (19) take place the radiation formation length 2, is much larger than the
wavelength 2&o.
Using the method descrived in $ II, we can find out the solution to Maxwell’s equations
(1) that satisfies the correct boundary conditions on each interface. From this solution we can
see that so long as the distance between two boundaries is of the same order of Z,, radiation
intensity peaks appear at certain frequencies w and angles 8. For example, in the case of a flat
plate of thickness a in vacuum the formula for XTR intensity frequency-angular distribution is
(21)
Here d2W~~(+)(w,B)/dwd6 is intensity distribution of XTR formed on one boundary (13),
Fplate describes the effect of interference between two boundaries of the plate:
Fplate =
(1 -e-na12)2 +4e-7ai2sin2 g,
(22)
and 77 is the absorption coefficient of the plate matter
n=ENw.
c
(23)
In the case when N plates (the thickness of each plate is a) constitute a regular stack with
vacuum spacing b the XTR intensity frequency-angular distribution is
d”i4&,(w,
L9) =
d’~~g,(w,O)
dWd0
where &tack
dwd0
F
stack,
(24)
describes the effect of interference between plates:
(1 - e- Ntlal?)? + qe-Nqa/a sin”
Fstack
(25)
=
(1 _ e_VQ/2)2
2,
=
+ dje-oQ/? sin”
2av
w(y-’ + 02)
It can be seen from (21) and (22) that at
(26)
RADIATION OF FAST CHARGED PARTICLES IN MEDIA
328
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a
z, =272+1
(27)
(n is an integer) intensity peaks appear in plate XTR. From (24) it can be seen also’ that at
$+52m
m
”
(28)
(m is an integer) the interference factor Fstack achieves its maximum
’2 2
F,rylzlk = 1 - e-Nga
1
e-W/2
(
> .
(29)
If Nya < < 1 (radiation absorption in plates is negligible) we have
max
Fstack
x
N2.
(30)
If the stack is irregular, i.e. plate thicknesses a and vacuum spacings b are random and independent, the frequency-angular distribution formula of the average intensity of XTR becomes9
dw-(+)(w
e>
tr.st
7
dwde
=
d”@&4
dwdb’
0)
(31)
F
II-.st,
1 - QN (I+ Q)/2 - ha - [Q - h,(l+ Q)/2]ht,
Fjr.st = 2R.s -
1-
1-Q
h,hb
(32)
+(I - h&Q - h&b[QN - (hahb)N]
(1 - h,hb)(Q - h&b)
h, =
(emi+‘la),
hb =
1
’
(e-+zb),
(33)
Q = (e-q4),
,,=f-vzz,
C
w
w
p2= y--case
c
.
Here (...) means average value of the corresponding quantity.
Analyzing Eq. (31)-(32) we see that with the increase of medium irregularity interference
peaks in XTR frequency-angular distribution become smoother (Fig. 2).
IV. QUASI-CHERENKOV RADIATION
It was metioned in 6 II that VCR cannot take place in X-ray region. But in single crystals
X-ray peaks still appear, because the secondary waves emitted by the atoms in the periodic array
interfere coherently at certain frequencies and angles when a charged particle passes through
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329
d--$4 0)
hwdwd6
(keV_l
)
2
3
4
5
6 (IO-~ rad)
FIG. 2. Intensity angular distribution of XTR formed in an irregular medium’: RO = 4 keV, y = 104, (u) =
7pm, (b) = 410pm, N = 50, fiwp = 20 eV. Different curves correspond to different degrees of ir-
regularity: from 4.5 % (dotted curve) to 70 % (solid curve).
the medium. This possibility of radiation peaks generation was noticed by Ter-Mikaelian in
1961. Garibian and the author carried out a detailed theoretical investigation of this problem
and derived the frequency-angular distribution formula of the radiation intensity 6 (see also’) .
Since the nature of this radiation is interference enhancing of secondary waves of lattice atoms
under the influence of the passing particle, i.e. is the same of VCR, it was later called quasiCherenkov radiation (QCR).
The simplest case is the one when a particle passes through a thin crystal plate at a constant
velocity. If the secondary waves of lattice atoms are much weaker than the proper field of the
charged particle, they may be treated as a perturbation. In this case (the so-called kinematic
approximation) the frequencywB and the propagation direction nit of QCR peak are determined
by the Bragg equation
ilh =
c&
no •+ WE3 .
(34)
Here no = v/v is the direction of particle motion and Kjr is the reciprocal lattice vector, multiplied by 2.z (It = 1, 2,...).
Thus QCR of a single crystal constitutes the Laue pattern, in which the central spot is
directed by no and the lateral ones by nh. This situation is similar to the diffraction of “white”
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RADIATION OF FAST CHARGED PARTICLES IN MEDIA
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X-rays in a monocrystal, because the transverse components (those perpendicular to the particle
velocity) of the electric and magnetic fields of a high-energy charged particle are much greater
than the longitudinal ones, similar to that for free electromagnetic waves, and consist of a wide
frequency spectrum (see (3)). In the kinematic approximation the formula for the radiation intensity distribution of the central spot is
d’l’i’~~&.
d&o
0)
4e’Lci4pO’ sin’[wcl(O” + 1-?)/4~]
(02 + y - ? ) 4
= ir?c./
’
(35)
(B < -c 1, y 1 w/6+ > > 1, do = &ZM$). It is not difficult to see that we can obtain the same
formula by putting in (21)-(22) the approximation a < c 2, (E” < < wP2/w”). This means that
the central spot of QCR is nothing else but XTR.
The formula for the laternal spot radiation intensity distribution is
dwdo
where the Bragg angle 0~ is half of the angle between no and n/,:
f?B = Sill
(37)
t is a small quantity of the order of y“ ,8’ or 1 w - wB j/wB andxjl depends on the crystal structure
and temperature (this quantity figures also in X-ray diffraction theory). Generally speaking, the
greater ]KI, 1 is, the smaller ]xh I becomes. In (36) the polar angle 8 is measured from the Bragg
direction nh, and the azimuthal angle $ is measured from the plane (n,,*no).
By virtue of (36) we can estimate the angular and frequency widthes A@ and Aw of QCR
lateral spots of a thin crystal:
A0 N y-l,
Aw -
2.
a
(38)
Integrating (36) over 8, @ and w we obtain the lateral spot intensity:
(39)
(m is a unit vector perpendicular to the crystal plate surface).
We see from (39) that lateral spot intensity HJ’QCD/~ of QCR of a thin crystal is proportional
to the path length al(ng . m) of the particle within the crystal.
While the crystal thickness is of the order of the extinction length l,,t or greater:
u > I& - WIlShl
-------,
W;
-
__--
(40)
L_-
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331
the secondary waves are not much smaller than the electromagnetic field of the charged particle.
So we cannot use the kinematic approximation. We must consider the interaction of lateral spots
with the central one (dynamical approximation). A formula of lateral spot radiation intensity
distribution rather more complicated than (36) was obtained (see Ref. 6, 5). The analysis and
calculation of this formula showed that the dependence of the lateral spot intensity WQCD, on
the crystal thickness (I is not simple: because of interference of QCR formed in different parts
of the crystal WQ,D, does not change with a/(nu * m) monotonously*‘.
The angular and frequency widthes A8 and Aw of QCR lateral spots of a thick crystal are
A0 -
kf!? - I()-?,
Aw -
2 - 1o-3 - lo-“wn.
WB
(41)
Thus QCR is a highly directed and highly monochromatic radiation. Under favorable conditions
every charged particle produces about lo-’ -10” photons in one crystal plate.
V. CHANNELING R A D I A T I O N
Entering into a crystal at small angles relative to crystallographic planes or axes charged
particles may move within these planar or axial channels. In this case particles oscillate in channels and thus emit electromagnetic radiation. This kind of bremstrahlung was first noticed
theoretically by Kumakhov” and is now refered to as the channeling radiation (CR). Many researchers calculated the characteristics of CR in different cases of planar and axial channels for
either electrons or positrons (see, e.g., Ref. 12). It was shown that for high-energy electrons and
positrons CR is quite hard (fiw is of tens of MeV and larger) and its spectral intensity is higher
than ordinary bremstrahlung in a similar amorphous medium approximately by one or two orders of magnitude. CR emitted by oppositely charged particles (with equal other parameters)
are different. For example, CR frequency spectrum of positrons (in planar case) is much narrower than that of electrons. Cases when particles move just above the potential barriers (SO13
called the quasichanneling regime) were considered in detail also. In particular, it was shown
that radiation emitted by electrons in both cases of axial channeling and quasichanneling has intensities of the same order of magnitude.
In investigations of dynamics as well as radiation frequency-angular characteristics of
charged particles at channeling or quasichanneling in a real crystal it is necessary to take into
account the field of all crystal axes. Besides, usually it is important to consider the influence of
incoherent multiple scattering of particles on the medium nuclei and electrons. For this purpose
a productive method of numerical simulation was developed. This method is based on solving
particle motion equations in a crystal atomic field averaged along axes or planes (field of “continuous” axes or planes)“. The particle incoherent scattering on thermal oscillations of nuclei
and medium electrons is simulated by means of stochastic differential equations 15..
,
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RADIATION OF FAST CHARGED PARTICLES IN MEDIA
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XT(x, y)
dv, = - moydx dt + gr(x, y)dW (t)t
dv, = _wx7Y)
mordy dt + &,~)dj/ryiW,
(42)
dx = v,dt,
dy = v,dt.
Here mu is the rest mass of the particle moving under small angles relative to crystal lographic
axes (parallel to axis z), U(x, y) is the particle potential energy in a field of continuous axes:
U(x, y) = $ JdS &&)k
* 0
U,,,(r) is the particle potential energy in the crystal averaged over atom thermal oscillations, dz
is the crystal lattice period along axis z, &VI(~) and dWz(t) are random quantities corresponding
to the so-called Winner process:
dWi(t)dW’(t) = 6ijdt.
aa (a = x, y) are connected with mean square changes of transverse velocity
where the interval At of averaging is such that during this time the particle travels a distance
much larger than atomic dimensions but much smaller than distances on which the particle
potential energy changes essentially.
It is often convenient to describe the particle state by means of tranverse energy
&A =
Y(vZ + v;, + U(x,y).
Because of incoherent scattering the particle tranverse energy EJ_ is not conservative. The successive solution of stochastic differential equations (42) showed that the projection of particle
trajectory onto the transverse plane (x, y) has a complicated chaotic view. Particles repeatedly
pass from a channeling regime (~1 c Uo, where Uo is the channel depth) to an above-barrier
one (quasichanneling one, EL > Uo) and vice versa.
The calculation showed also that the mean squared angle of particle multiple scattering
at its planar channeling and quasichanneling in a crystal differs significantly from the analogous
quantity in an equivalent amorphous matter. Incoherent scattering of electrons at transverse
energy of the order of the height of potential bsrricr (~1 = Uu) is suppressed because of “hang-
-.____.._ _.-
VOL. 30
C. YANG
333
ing” of electrons in the space region where the charge density is minimal. On the contrary,
positrons with EL = U, “hang” nearby crystallographic planes that leads to intensification of incoherent scattering many times as compared to the case with a disoriented crystal.
From obtained trajectories one can calculate the frequency-angular distribution of the
radiation intensity by using the well-known formulae of electrodynamics. Integrating this distribution over angles one obtains the frequency spectrum. The resultant radiation frequency
spectrum may also be obtained approximately by averaging the spectrum for a particle of a given
transverse energy EL over ~1. Results of these two approaches were compared” and the difference between them was found to be not significant.
It is of interest to find out the influence of different external fields on the particle motion
and the radiation characteristics in channeling and quasichanneling regimes. InI6 the influence
of longitudinal elastic deformation waves (sound or hypersound) on the motion of planarly channeling particles was investigated. It was pointed out that the anharmonism of particle potential
of real crystals plays a principal role in a resonance phenomenon when the frequency of the external modulation of the crystal potential approaches the double value of the proper frequency
of particle transverse oscillations in a channel. The anharmonism leads to a nonlinear equation
of motion and, in particular, to amplitude dependence of frequency of particle proper transverse
oscillations. This dependence involves departure from resonance when amplitude changes. The
solution to the nonlinear equation of particle motion and the numerical simulation showed16 that
the anharmonism leads to a “contraction” of the particles transverse oscillation amplitudes to a
stationary one which is a function of the sound frequency. This phenomenon causes an essential
deformation of the CR spectrum.
VI. EXPERIMENTS AND APPLICATIONS
Optical transition radiation was experimentally observed for the first time by Goldsmith
and Jelley17. Experiments on OTR of nonrelativistic particles were also carried out by Boersh,
Dobberstein ef al. (West Germany), Michalak (Moscow), Harutiunian ef al. (Armenia), Arakawa
(USA) etc. These authors have thoroughly investigated the intensity and polarization of OTR
in the visible and infrared regions and their dependence on particle energy and incidence angle
for many metal and insulator interfaces. The experimental results were found in good agreement with theory (see Ref. 18-20). But when the particles impinge on the interface at small
glancing angles a radiation much stronger (for one or two ordres of magnitude) than the
theoretical prediction was experimentally registered. It was found that this anomalous radiation
is unpolarized and is due to surface roughness.
Alikhanian ef al.“l first suggested several experimental methods for registration of XTR.
In the 60’s a number of XTR experiments were carried out in Armeniaz2 and USA13. L. C. L.
Yuan (USA) ef al. registered XTR generated by positrons with energy 2 GeV e/ = 4000) in a
-_.. .,- _..-.
334
RADIATION OF FAST CHARGED PARTICLES IiK MEDIA
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stack of aluminum foils (a = 25 /tm, b = 0.3 mm, N = 231)‘3. It was confirmed that in the
range of y = 1000-8000 the total energy of XTR (hw = 3-270 keV) depends on y linearly,
Making use of a spark chamber, Alikhanian, Lorikian et ~1.‘~~‘~ obtained photographs of
XTR photons (Fig. 3) generated by electrons of energy about 5 GeV. They confirmed also that
while electron energy increases from 1.2 GeV to 2 GeV the number of XTR photons increases
approximately linearly. Alikhanian et 01.‘~ measured the angular distribution of XTR of
electrons with energy from 0.4 to 4 GeV in a stack of polyethylene films. In this experiment a
CsJ(T1) crystal scintillation counter with a small hole in its center was used for detection. But
because of scattering of electrons in the stack the experimental errors might be quite large.
Frequency spectra of XTR were measured for the first time by L. C. L. Yuan.23 Somewhat
later XTR frequency spectra of regular plate stacks in different cases were measured with details
in Armenia27*28 and USA’9930. The experimental results agreed with theoretical calculation
quite well.
XTR frequency spectra in irregular medium (plastic foam) were measured by Alikhanian,
Lorikian et a1.26 At CERN Fabjan3’ measured frequency spectra of XTR formed by electrons
with energy 1.35 GeV in porous material. Experimental results were compared with theoretical
formulae9 and a good agreement was found (Fig. 4, 5).
An important application of XTR is the construction of detectors of high-energy particles.
FIG. 3. A photograph of clcctron Irajcctory (111~ slr:light line) and XTR photons obtained in a spark chamber2’. A mqnclic ficld applied in front of lllc spark chamber dcflcc~cd the electron trajectory, so
the photons ctppcarcd only on one side of il. ‘I‘hc clcctron cncrgy was about 5 GcV.
A-
-
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VOL. 30
5
FIG. 4.
335
20 30 40
10
fiw (keV)
XTR frequency spectra in different regular stacks of polypropylene foils”: (a) u = 82pm, N = 200;
(b) (I = SO,~lrn, N = 250; (c) (I = 16,um, N = 1000; b = 1.4 mm. Solid curves (theory) and triangles
(experiment) correspond to electron energ 9 GeV; dashed curves (theory) and circles (experiment)
correspond to eleciron ener,g 5 GeV.
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RADLATIOK OF FAST CHARGED PARTICLES IN MEDIA
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F I G . 5. XTR frequency spectra of electrons in porous material (ethafoam)31. The solid histogram refers to
experiments, the dotted one to the theorg.
Parameters of XTR depend on Lorentz-factor y of charged particles, so by measuring these
parameters (e.g. XTR intensity) one can distinguish particle mass or Lorentz-factor.
In the middle of the 70’s almost simultaneously at Yerevan Physics Institue (Armenia) and
the University of Maryland (USA) apparatuses using XTR detectors were built for cosmic rays
investigations. The Yerevan apparatus3’933 named PION was set up on Aragatz mountain at the
level of 3250 meters. PION was designed to investigate the interaction cross-section of cosmic
pions and protons of energy 300 GeV and higher with iron nuclei. After a number of improvements PION is still in use now. The apparatus of the University of Maryland% is similar to
PION. The ratio of numbers of cosmic pions and protons with energy beyond 100 GeV
measured by means of this apparatus is in agreement with that obtained at PION.
XTR detector was used in proton-proton collisions experiment at CERN Intersecting
Storage Rings (ISR) for separating electrons and positrons from pions among products of collisions3’ and thus for confirming the existence of J/q and Y particles.
Besides, L. C. L. Yuan et al. used superheated superconducting granules in magnetic field
as XTR detector. 36 They tested this detector at accelerator DESY (West Germany). One of
the international research groups at CERN built an XTR detector utilizing drift chamber
capable of discriminating pions from kaons of energy about 140 GeV.37-3g
Vorob’e v et al. (Tomsk, Russia)40 and R. Avakian et al. (Yerevan, Armenia)41 for the first
time successfully observed QCR generated by electrons of energy 1 GeV and 4 GeV in diamond.
The spot frequencies 0~ and angles 2813 relative to the direction of electron motion measured
in these experiments were in good agreemenl with the theory (see (33)). But the spot intensities
VOL. 30
C. YANG
337
were weaker than calculated by the theory. R. Avakian, Mkrtchian et al. found42 that under influence of supersonic waves or temperature gradient the QCR intensity increases noticeably.
QCR of a stack of crystal plates may be used as a source of highly directed and
monochromatic X-rays. The region of photon energies beyond 20 keV (wavelengthes shorter
than 0.5 A) is of interest.
ACKNOWLEDGMENTS
This review paper is based on works done in collaboration with G. M. Garibian, A. R.
Avakian, L. A. Gevorgian, M. A. Aginian and others at Yerevan Physics Institute of Armenia.
The author is grateful to the National Science Council of the Republic of China for financial
support.
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