JAERI-Conf 95-021

PB49
Novel X-ray Source Using Collisions of Circulating Relativistic Electrons
and a Wire Target
Himnari Yamada
Faculty of Science and Engineering, Ritsumeikan UniversityandPRESW, Research and Development Cmporation of Japan
1916 Noji-Cho, Kusatsu-City, Shiga 525, Japan

Abstract
The novel method far generating brilliant x-:ray beams ispmposed, in which inelastic collisions of circulating relativisticelectrons and a thin wire target are used. High brilliance of this newphoton source stands on narrow angular divergence due to thekinematics of relativistic electrons, and repeatedly use of electmn
beams. The estimated brilliance of this source based on a 50 MeV
eleci:ron sto:rage ring is compa:rable to that of compact synchmtmn
light sources.

pmductivity will be significantly enhanced ill comparison with thecase using a linac and a thick target A thin target is useful tominimize absmption of x-:rays and electmns which muse heatingpmblem of the target The continuous injection of an eleci:ronbeam into the sto:rage ring at full energy is a way to compensate far
the lost beam and to keep a high, constant beam mnent We gain
yet another advantage when a thin wire target is used, because
effective x-:ray source size is detennined by the width of this wire.
2. Bremsst:rahlung yield

1. Introduction

X-:ray emissions are generated when electrons are
decelerated by either an electric or a magnetic fO:rce. classical x-:raytubes and mtating anode sources use atomic elec1rical furces, andsynchmtmn :radiation (SR) uses bending magnets or wigglers. Allof these sources generate continuous and incoherent spectra The
SR emissions are brighter than x-:ray tube emissions only because
SR emissions have a narrower angular divergence, but theinteg:rated total :radiated power is almost same fur both methods.
Note that the divergence is detennined by the kinematics of theeleci:ron beam regardless of what the decelerating fO:rce is. The
divergence is abou1t 1/y in either cases, where y is the Lorentz factor.
Using relativistic electmn beams is the key issue far achieving thenarrow angular divergence of x-:ray beams.
The bremsstrnhlung spectrum extends up to the incident
eleci:ron energy. This implies that 100 keV electmn beam isenough to pmduce 100 keV x-:rays. X-:rays are therefOre pnxluced
more efficiently with conventional x-:ray tubes than with SR
The above conside:ration leads to a simple idea far a novel x:ray source that uses collisions of circulating high-energy electmns
and solid targets in a sto:rage ring . The narrow angular divergenceis secured by the high eleci:ron energy. High energy x-:rays can beeasily gene:rated by the bremsstrahlung due to the inelastic
collisions inherent with this kind of source.
Using a thin target is also the key issue far present x-:raysource in onierto avoid inc'reaSing angular divergence ofx-:raybeam due to multiple scatterings. The electmn beam passing
thmugh the thin target is utilized repeatedly so that the x-:ray

As well known the differential cmss section ofbremsstrahlung has been quantum-mechanically calculated by
Bethe and Heitlerl, Shiftz, and others in the 1950's. A SU11ll11ai)'of theories and experiments is given by Koch and Motz.3. In onier
to evaluate the bremsstrahlung yield in comparison withsynchmtnm light, we define here the brilliance of the bremsstrdhlung as:
4Z(Z + !)1~a,I
d' N 8,137
dQdS ~ !.6E -19 sb ·n, ·x,dk

1r'~~-2 J,k x,xynes. o{!6fr'E;(l+fr2 ) 4.

sm{B)dB(Eo +E)' Eo +lln(EE" )[(E, +E)' E,E(l+fr2 ) 2k

E(l+fr2 ) 2 •4fr'E' ]}(l + fr,')'----- (1)where I is the beam mnent, nt and Xt are the target density andthickness, k, E0 , andE are the x-:ray energy, the incident eleci:ronenergy, and the scattered eleci:ron energy measured in the eleci:ron
rest of mass energy units, respectively. The {} is defined as{} = 8 · Ea , where 8 is the angle between the directions ofphotons and incident electmns. The integ:ral in eq.(l) is carried out
over 0-8sr We assume 8Br = l)y which covers the peak in the
angular distribution amund O.S)y. Thus, this definition gives
averaged brilliance, but not the peak value. The brilliance is anonnalized value with the source size Xx · Xy where 'XX' Xy are thehorizontal and vertical target size or beam size, whichever issmaller. While the target size is smaller than the beam size, the-386-

JAERI-Conf 95-021

brilliance is detennined by the target size. Please note that in eq. (1)we take the efifx-tive beam mrrent, (/. *atfSb} where at is the x-:raysoun:e area which is determined by the target size, and Sb the beamsize.

Table 1. Machine parameters of a 50 MeV elec1ron storage ringand Brennsstrnhlung intensities produced by the scattering of thestored beam and targets are shoWIL Photon intensities are
1 tedt"or lOOkeV x-:ray.
calma~

Machine p!l""diTlete!s3. Beam mrrent
In the next we estimate the obtainable ring beam mrrent
resulting fiom rollisions of the beam and the target material with arontinuous beam injection. The time evolutiem of the stored beam
mrrent (df1dt) may be expressed by the following equatiem:
2.
d!
.,dt = R . E • I Ot. f- 1-"'-'T- Yl/II0.

11(2)Eledron energy !MeV]

50O!bitrndius [m]0.15~"'RIOOS'Iurn, eledron [eV]3.fB

n-valueO.Dl

RF voltage [keV]

120.00Hannoni:s8

RF freque!Ly245E-tm

Horizontal dampingrnte

50[tiD:;]•roTDll'rllek halflire [=:]at

The fust term of the right hand side is the beam growth :rate by
injection, which is given by multiples of the injectiem :rate, R; , thetotal injediem effidenc-y, E; peak mrrent, Io , the du:ratiem in which
the beam is accepted by the storage ring,Ot , and the frequenc-y ofth,e dn.;ulating beam, f . The mrrent decay :rate can berepresented byfust- and seamd-ordertennsofJwith theroeffidents !.1. and 11 The meanings of these :rate roeffidents will
be clarified in the following.
The stored beam decays by two prindpal efifx-is. One efiectis Touschek scattering which is lmge-angle scattering caused byCoulomb repulsiem between electrons in a bunch. The other efifx-t
is eh1ron-target scattering as the fonnula is known by the problem
ofgas scattering in a storage ring. In eh1ron-target scattering bothinelastic and elastic scattering em target nuclei ()C(.,'l.IT, with inelastic
scpttering causing bremsstrahlung.
Elastic scattering em nuclei of the target leads to angular kickfar the betatron motiem of the elec1ron beam. If the induced
betatnm amplitude exceeds the transvcrse acceptance of the ring, Ac the beam will be lost The total cross Se<.,tiem fiJTthis process ise~pressed by:4lOA
9Horizontal beamwidlh[mm]05

VeJOCal beam widlh[mm]9Burrl!lengtll[_II1Il1]
8CfuilC-wireW-wiretaiget density [I1UillbeJfm3]

1.13E+29

1.13E+29

6.2'ill+28

Tmgetwidlh [!illl]-100

1010100

10

9.73E-30

9.73E-30

129E-27

Tmget lhidme;s [!illl]
Cros<;~on [m2]Radiation looieledron [eV]1.07Et03

1.07E-tD4

7.87E-tD4

Beam loo;rnte by inellsic

7.64Et03

2ffiE+ffi

1.2'illt03

26.'ill-tD4

7.04Et03

5.16Et03

s:at. [tiD:;]

Beam I= rnte by ellsics:at.

f/&xl
JnjociDrp!I""diTleleis
Jnjedionrnte [Hz]50

PeakUliTel1! [A]10

Jnjedion efficicrLy

6.0E.al1ntegrntedbeam UliTel1! fAl

0379

1.43

202

PhotonfluxfurlOOkeVxrny

5.91E+l0

5.91E+l0

6.13E+l0

Bnlliaoce fur lOOkeV x-rny

1.79E-tm

5.rxiE+l0

5.2'ill+ll(3)
where Z is the atomic number, re is the classical elec1ron :radius,and ( f-1) is either the horizcmtal or vertical beta1ron amplitude,
whichever limits the beam drculation. The transvcrse acceptanceis actually limited by either the half:.Chamber aperture or thedynamic aperture, b, at the place where the betatnm amplitude is [30 . The acceptance is then given asAc=iJ21[30 , and ( f3) = f3 o •Note that this cross sediem decreases quad:ratically with incTeasing
electnm encrgy .
Bremsst:rahlung is an inelastic scattering process that leads toan encrgy loss for the drculating elec1ron. The elec1ron will be lost

if the encrgy loss exceeds the limiting longitudinal momentum half·
aperture, ( flp I p) max of the ring that is proportiemal to the :radiofrequenc-y bucket height The total C'IOSS Se<.,tiem for this inelastic
pmcess leading to the beam loss is given by:S(_4Z\ :!.[t11 (183)J[t111/J
20 Rr -'>

1.17 3Z1(t:J.pjp)max~]·(4)8Note that this m:JSS Se<.,tiem is independent of the electn)n energy.
The total beam lt:JSS :rate, f.l., due to the above elastic andinelastic scattering can be expressed as:-387-JAERI-Conf 95-021

Omsequently the ma'<irnum obtainable x-ray production isdetermined by the ma'<irnum output power of the ii1jector.

(5)

4. Cbnclusion
where 1Zt and Xt is the target density and thiCkness, respectively.
The at is the x-ray soun:e area which is determined by the target
size when it is smaller than the beam size, sb. Ifthe target size islarger than the beam size, at is equal to the beam size. The
calculated beam loss rates fm a 50 MeV ring with various target
materials and shapes are shown in Table. 1. A half:.momentum
apertureof (L\VPkax=0·06andtheverticalhalf-chamber
aperture ofb=3 em is assumed in these calculation. A 10 !lfll-thickcarbon foil gives beam loss rate of7640/sec fmthe inelastic and26500/sec fmthe elastic scattering. In the case of 10!lfll~ tungsten
wire, these are 1250/sec and 5160/sec, respectively on assumptionofRMS beam size of9 x 0.5mm. Jn(..'reaSiog beam size simply
leads to reducing beam loss rate, and consequently in~ ring
cmrent acoording to eq. (2) and (5). The maximum beam current
is reached when the beam injection and the beam loss are balanced.
Then the maximum beam current is obtained by solving eq. (2) fordl!dt='J.
We summarize the resulting mmcimum beam (..mren1: andthe machine paramete!s of a 50 MeV electron storage ring in Table
1. In this cal(..'Ulation we assumed 50A peak cmrent and IO Hz
injoction rate. We assumed an injoction efficienq' of Ej='J.6 which
is ronsetvative fOr a resonance ii1jection method. 6 We assumed a
10 !illl thick cabon foil, 100 !lfll carbon wire, and 10!lfll tangsten
wire taget, but the thiCkness is unimportant fm estimating themm<imum x-ray yield, because the effect of the target thiCkness
and density are canceled out in this calculation. The x-ray (..TOSSsection is proportional to the target thiclmess and density, but themaximum beam current is invcrsely proportional to these target
parameteJ:s. The x-ray yield is the multiple of the (..TOSS section andthe beam current The width is important for higer brilliance. The
beam size is unimportant fOr the total x-my yield It may growth
due to the scattering, but the total x-ray yield will be unchanged.

In summacy, we believe that the use of inelastic rollisions ofrelativistic electron and of solid targets is a promising new way togenerate brilliant photon beams ranging from soft x-ray to beyond
100 keV x-ray. The size of this novel soun:e must be very
attrn.<.:live compared with rompa(..t SR soun:es.
It is worth to point out that if the size of the ring is notproblem, the higher encrgy eloc1nm stornge ring is advantageous.
For instance a300MeV ring generates th~ds times brighter xray beam, since the angular distribution is less than 1/6, the beamloss rate by elastic scattering is reduced 10 times, and the beam size
is reduced 100 times.
In this paper we didn't include otherrndiation mechanisms
like trnnsition and Cerenkov rndiations. It is lmown that thestrength of trnnsition radiation may reach the same level as~'and that photon ene.tgy :from 50 MeV electrons isavailable up to a few keV. It is also lmown that stacked fulls
generate roherent x-ray beam. We therefore expoct that the new xray source will produce much more power than we have de5(..Tibedabove.

References
1. H Bethe and W. Heitler, Proc. Roy. Soc. (London) A146, 83(1934).
2. LIS~ Phys. Rev. 83, 252(1951).
3. H W. Koch and J.W. Motz, Rev. Mod. Phys., 31(4), 920 (1959).
4. J. LeDufl: Nucl fustrum. Methods A239, 83 (1985).
5. M.S. Zisman, S. Clmttopadhyay, and J.J Bisognano, Lawrence
Berkeley laboratory Technical Report, I.BL-21270.
6. T. Takayama, Nucl.Instrum Methods B24/25, 421)(1987).

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