Status Report on the LACARA Experiment
Sergey V. Shchelkunov*, T.C. Marshall*, J.L. Hirshfield*'+, Changbiao
Wang*, M.A. LaPointe*'+
^Department of Applied Physics, Columbia University, New York City, NY 10027
department of Physics, Yale University, P.O. Box 208124 New Haven, CT 06520-81:
+
Omega-P, Inc., 199 Whitney Ave, Suite200, New Haven, CT 06520
Abstract. LACARA (laser cyclotron auto-resonance accelerator) is an 'advanced concept'
vacuum laser accelerator of electrons that is in the design and construction phase at the
Accelerator Test Facility at Brookhaven National Laboratory. As a bunch moves along a
solenoidal magnetic field (~ 6T), it is to be accelerated from 50MeV to ~100MeV by interacting
with a 0.8TW Gaussian-mode optical beam provided by a CO2 10.6um laser system. We
present a system design here for the electron as well as the laser optics to accomplish this
objective. The laser optics must handle 5J and be capable of forming a Gaussian beam inside the
solenoid with a 1.3mm waist and a Rayleigh Range of 50cm, followed by a dump. The electron
optics will transport a bunch having input emittance of 0.015mm-mrad and lOOum waist through
the magnet. Emittance- filtering may be necessary to yield an accelerated bunch having narrow
energy-spread. The design presented shows that a useful test of this concept may be done in a
way taking into account the specific features and requirements of the ATF facility. It is expected
that the experiment will be assembled by October- November 2002.
INTRODUCTION
LACARA is a vacuum laser accelerator of electrons, which uses a TW, circularly
polarized Carbon Dioxide laser and a solenoidal magnetic field for acceleration. The
interaction may be understood as follows. Laser photons will travel in the same
direction as the electrons, and therefore the Doppler-shifted laser frequency in the
electron rest frame is yo)( 1 - n-(3z), which should be equal to the electron cyclotron
frequency Q0 = eB/m so that the laser energy may be transferred to the electrons. If
the magnetic field is constant during the motion of the electron, then one can
appreciate that an increase of y and an increase of (3Z is compatible with a fixed
laser frequency co. The behavior of the index of refraction n (see below) on position
(z) will determine the details of the energy gain. Since both (1 - n) and ( 1 - j8z) are
«1, it follows that Q/co~ l/2y.
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
349
A useful feature of this device is the utilization of high laser power in the form of
a Gaussian beam, which is readily produced by the laser system. Consequently,
there is no need to further process the beam cross-section prior to utilization of the
laser power. Simple lenses and planar mirror optics can be used, permitting the
problem of dealing with high radiation load to be solved through a simple
enlargement of apertures.
The LACARA does not require a prebunched beam, and all injected electrons can
experience nearly the same acceleration history [1,2]. Operated without a tight laser
focus, LACARA is able to provide continuous acceleration in vacuum over several
Rayleigh lengths. The scheme is not be limited to being a "y - doubler" - the
relativistic energy factor can be increased by more than a factor of two in a single
stage. LACARA uses an axial static magnetic field to maintain synchronism
between electrons and the rotating electromagnetic field of a circularly- polarized
laser beam. LACARA is currently being installed at ATF, Brookhaven [3]. The
accelerator will utilize 800 GW 10.6- jim CO2 Laser power. The laser spot in the
focal plain is chosen to be 1.30 mm, which corresponds to the Rayleigh length of 50
cm. The bunches of electrons, with 200 - 600 pC per bunch, will be accelerated
from 50 MeV to 90 MeV in a solenoidal field which has overall length about 1.8m.
The energy spread is expected to be as small as 3 %. In this paper we shall
concentrate our attention on matters of beam transport and diagnostics through the
solenoid, where high precision is needed to extract an accelerated beam with
acceptable quality.
This project is a collaborative effort of 4 organizations: the Applied Physics
Department of Columbia University, Omega-P, Inc., the Beam Physics Laboratory
of Yale University, and the Accelerator Test Facility of Brookhaven National
Laboratory.
FORMULATION
The laser power P and the amplitudes for the electric and magnetic fields of the
Gaussian circularly polarized laser beam [4,5] are connected
-] = 15.5 - I 0 .
m
W[mm]
Bo[T]=5l.l •
W[mm]
=W.7
[GVtm],
=35.6[T],
(1)
(2)
where the computed numbers are appropriate to P = 800 GW, W = 1.3 mm.
In the formulae (1-2) W is the waist at the distance Z from the focal plane:
w =wo-l+(z/zR)
350
(3)
The phase advance for the circularly polarized wave is given by:
2
/2-R-O
(4)
with
(5)
R(z)=z
The components of field in the direction of propagation are comparatively small
[4,5]. Thus the electric and magnetic field can be thought of as approximately
transverse. Suppose for a moment that we have a purely transverse linearly
polarized electromagnetic field. If there is a charged particle in the field region then
the action of electric and magnetic field will eventually force the particle to move in
the direction orthogonal to both electric and magnetic components, yielding final
energy gain in this direction. However, this acceleration is limited because the field
region is localized near the axis of the system and the particles have some nonzero
transversal speed, which causes them to leave the place where considerable energy
gain can be achieved. The presence of transverse velocity components is an intrinsic
property of the bunch described by the final emittance. Thus, one is led to the use of
a solenoid, where particles will gyrate along the field lines. The EM-wave with
linear polarization in the particle reference frame then must rotate in the laboratory
reference frame. Fig. 1 shows schematically the orientation of the laser beam, the
particles, and the solenoidal field.
Circularly
Polarized
Laser Light
Laser Fields
Envelope
e-Bean
Laser
2 - 3 Rayleigh
Lengths
FIGURE 1. LACARA schematic.
The magnet axis and laser beam centerline coincide.
In order to have constant acceleration the wave phase advance along the particle
path must obey
351
A
dt
Y
'
(6)
a • /?
where Qo = ——~ - the nonrelativistic gyrofrequency of electron inside a solenoid,
me
and y is the customary particle relativistic factor.
This can be represented as
where the last part follows fromj8r « j8z.
The axial and radial refractive indexes are given by:
nr = r/R,
1 w2, + M z ? - z 2 ) - r 2 ^ 1
2
" r ^ l -2
^'-z-R
^ + T2'- Z22-R
~ 1 -^-^
P2
2 z-R
(8)
W
The resonance condition (6) can be maintained along the orbit for an accelerated
electron if the magnetic field is tailored in space to track the variation in y.
However, one may maintain an "average" resonance through space by keeping the
magnetic field unchanged. Thus, one concludes that a simple uniform magnetic field
is sufficient; this greatly reduces the cost and complexity of the superconducting
magnet, and expands its flexible use.
A numerical simulation is essential to fully investigate what can be achieved under
such circumstances. A special code, CARA-code, was designed [2]. It has been
tested in various simple situations to insure that the numerical noise has negligible
impact on the physics investigated. The CARA-code operates on an ensemble of
macro particles, tracking each one of them through a solenoidal magnetic field in the
presence of a Gaussian wave as described in (1-5). The initial distribution of those
particles in both coordinate and velocity spaces is Gaussian, as is also the case with
the electron beam at ATF, Brookhaven. The acceleration channels are commonly
described in terms of the so-called, Twiss parameters: PT, Y T = (1+ CXxVPx,
Or = -(l/2)-3pT/ 3s, where s denotes the coordinate along the beam line [6,7].
Using the usual expressions for the second moments one the works out that the
particle distribution in the transverse phase space is:
00)
352
where ex, ey are the non-normalized rms emittances.
This integrates the entrance point of LACARA simulated by the CARA-code into a
given beam line.
The integration of the exit point of LACARA with a channel downstream of the
LACARA solenoid is made on the basis of following relationships:
<x2>
yz
nix
=-CCTs
(11)
where one uses the fact that LACARA accelerates a round electron beam
The emittance is given by:
<o>y>2
(12)
where the last term reflects the fact that both transverse motions inside a solenoid
are coupled. The formulas (11-12) allow description of the electron beam after
LACARA again in terms of the Twiss parameters.
If after acceleration one takes a snapshot of the transverse particle positions at one
plane (with "exposure time" of one optical cycle), an O-ring or donut-like image
(Fig.2.) results.
At the beginning of the acceleration the Lorenz force is pointed along the
direction perpendicular to the beam centerline, and simply displaces a particle off
axis. Usually, the length of an electron bunch is much longer than several optical
wavelengths, and consequently particles enter with different relative phases and are
displaced transversely into different directions. (One should notice that the
emittance given by (12) describes the entire effective donut area.) Another
contribution arises from the increase in mass of the accelerated particle. The
growing angular momentum pushes the particle away from the magnetic axis inside
the solenoid, and this is not compensated for when the particle leaves the solenoid;
thus there is further radial shift.
The formula (7) can be rewritten as:
Y'Zr'C
(0
where the last term is the leading contribution up to y ~ 385. At y ~ 385 both terms
equal to each other, and the magnetic field achieves its minimum of 2.63 T. The
resonance magnetic field goes back to 4.00 T at y ~ 1000, taking ZR constant. Thus,
using LACARA for high-energy acceleration seems feasible because it does not
require a very strong magnetic field.
3000
3000
2000
2000
Z, microns
1000
1000
o
0
N
-1000
-1000
-2000
-2000
-3000
-3000
-3000
-3000
-2000
-2000
-1000
0
0
1000
1000
2000
2000
3000
3000
X, microns
microns
FIGURE 2.The
2.The "snapshot"
“snapshot” of
of the
the transverse
transverse particle positions on
FIGURE
on aa plane,
plane, following
following acceleration.
acceleration.
Particles enter
enter into
into acceleration
acceleration with
with different
different phases
phases relative
relative to
Particles
to an
an electromagnetic
electromagnetic wave
wave (CARA(CARAcodesimulation).
simulation). The
The laser
laser power
power equals
equals to
to 800
800 GW;
code
GW; the
the electron
electron beam
beam atat the
the matching
matching point
pointisis
µm, and
roundwith
withthe
thewaist
waistaσxx,, yy==28
28 um,
and the
the non-normalized
non-normalized emittance
emittance is
round
is .0015
.0015 mm-mrad.
mm-mrad.
NUMERICAL SIMULATIONS
NUMERICAL
SIMULATIONS
An electron
electron beam
beam with
with non-normalized
non-normalized emittance
emittance εex == ε8z == .015
An
.015 mm-mrad
mm-mrad and
and
x
Z
initial
energy
E=50
MeV
is
now
available
at
ATF,
Brookhaven.
The
initial energy E=50 MeV is now available at ATF, Brookhaven. The laser
laser power
power
presently isis slightly
slightly above
above 30
30 GW,
GW, however,
however, itit is
presently
is expected
expected toto achieve
achieve the
the 800
800GW
GW
level
soon
after
laser
upgrading.
level soon after laser upgrading.
Considering acceleration
acceleration of
of an
an electron
electron beam
Considering
beam in
in general
general one
one may
may note
note that
that
due
to
a
finite
initial
diameter
of
the
beam,
different
particles
are
accelerated
due to a finite initial diameter of the beam, different particles are accelerated inin
different ways. This creates an energy spread and transverse emittance growth. If the
different
ways. This creates an energy spread and transverse emittance growth. If the
beam's initial diameter is reduced, then different particles should undergo very
beam's
initial diameter is reduced, then different particles should undergo very
similar motion in the laser field. Thus a reduction of the beam size will lead to a
similar
motion in the laser field. Thus a reduction of the beam size will lead to a
reduction in the energy spread and emittance growth. However, if there is a finite
reduction
in the energy spread and emittance growth. However, if there is a finite
initial emittance, then a reduction of the beam’s initial diameter leads also to a larger
initial
emittance,
then a reduction of the beam's initial diameter leads also to a larger
initial velocity spread. Consequently, different particles have different initial
initial velocity spread. Consequently, different particles have different initial
354
velocities and again are accelerated in different ways. Thus, if the emittance has
some particular value there will be some optimum value for the beam's initial
diameter in order to have the final energy spread and emittance minimized. It
follows that if one reduces the emittance simultaneously with the beam diameter
then one should obtain a reduction in the final energy spread and emittance.
The CARA-code simulation for an electron beam with the initial emittance 8 =
.015 mm-mrad, and energy of 50 MeV is presented in the Table 1. The electron
beam has its waist located at the entrance to the solenoid, and is circular there with
minimize the final energy spread.
TABLE 1.
Laser
Required
Power, Px=P y at
[GW]
entrance, [m]
30
0.68
800
0.68
Emittance,
final, [mmmrad]
.1387
.269
Energy,
gam
[MeV]
2.16
36.34
Energy
spread, final,
[%]
6.6
18
PTx=PTy,
final,
[m]
4.92
5.25
OCTx=OCTy,
final
-7.75
-8.00
In the Table 2 the simulation results for different laser powers and different initial
emittances are shown. The beam waist, -Je- PT =101 jim, at the entrance into the
solenoid is kept the same for all cases.
TABLE 2.
Laser
Initial
Power,
emittance,
[GW]
[mm-mrad]
30
.015
30
.0015
30
.00015
800
.015
800
.0015
800
.00015
4000
.015
4000
.0015
4000
.00015
Final
emittance,
[mm-mrad]
.139
.080
.080
.269
.184
.182
.432
.361
.358
Energy
gain,
[MeV]
2.16
2.10
2.11
36.34
40.74
40.80
74.63
91.00
91.00
Energy
spread, final,
[%]
6.6
5.7
5.7
17.9
10.7
10.4
37.8
28.5
28.7
Final
P T ,M
4.906
4.726
4.760
5.379
7.293
7.407
3.030
3.311
3.285
Final
Or
-7.729
-7.209
-7.262
-8.180
-10.885
-11.036
-4.472
-4.738
-4.706
While the initial emittance is changed by the factor of 10, then again by another
factor of 10, the changes in the final energy are minimal; the final emittance changes
by 25 - 40 %; the energy spread changes by factor of less then 2. This shows that
any reduction in the initial emittance must be accompanied by an appropriate
decrement in the beam initial diameter. Such cases are presented in Table 3, where
initially^£ - fiT = 46.3 jim for all rows.
355
rows (arbitrary
(arbitrary chosen,
chosen, -- not
not an
an optimal
optimal value
value
46.3 Jim
for all
all rows
µm for
ε ⋅ β T == 46.3
TABLE
TABLE3.3. Initially
Initially
Laser
Laser
Power,
Power,
[GW]
[GW]
30
30
800
800
4000
4000
Initial
Initial
emittance,
emittance,
[mm-mrad]
[mm-mrad]
.0015
.0015
.0015
.0015
.0015
.0015
for
for the
the emittance
emittance == .0015
.0015 mm-mrad)
mm-mrad)
Final
Energy,
Energy
Energy
Energy,
Final
emittance,
gam
spread,
spread,
gain
emittance,
[mm-mrad]
[MeV]
final,
[%]
[MeV]
[mm-mrad]
final, [%]
.0326
1.80
3.0
.0326
1.80
3.0
.092
45.33
3.7
.092
45.33
3.7
.193
108.8
7.9
.193
108.8
7.9
Final
Final
Pr,
[m]
β
T, [m]
4.685
4.685
12.795
12.795
5.773
5.773
Final
Final
OrT
α
-7.218
-7.218
-18.867
-18.867
-7.948
-7.948
§
0.3
6
0.25
5
0.2
4
beta, m
emittance, mm-mrad
With
800 GW
GW the
the
With the
the initial
initial emittance
emittance of
of .0015
.0015 mm-mrad
mm-mrad and
and laser
laser power
power of
of 800
minimal
28 µm.
Jim.
minimalenergy
energy spread
spread of
of 2.8
2.8 % is
is achieved when Jeε ⋅ fa
βT =
= 28
The
The emittance
emittance reduction
reduction can
can be
be made
made by
by the
the means
means of a pipe-like emittance filter
and
and itit will
will be
be done
done in
in the
the future.
future. The
The current goal is a proof of the principle
experiment,
experiment, which
which will
will be
be conducted
conducted with
with the initial non-normalized emittance, ε8 ≈~
.015
.015mm-mrad.
mm-mrad.
In
In Fig.
Fig. 33 isis shown
shown the
the emittance
emittance behavior inside the solenoid during the
acceleration.
acceleration. Fig.
Fig. 44 presents
presents the
the corresponding
corresponding beta-function
beta-function behavior.
0.15
3
2
0.1
0.1
0.05
1
•KX^/^/O^
0
-1.5
-1
-0.5
0
0.5
1
0
-1.5
1.5
length,m
m
length,
FIGURE3.
3.The
The emittance,
emittance, eεxx == eεyy,,
FIGURE
behaviorduring
duringacceleration
acceleration inside
inside the
the
behavior
solenoid. The
Theabscissa
abscissa zero-point
zero-point corresponds
corresponds
solenoid.
themagnet
magnetcenter,
center,and
and the
thefocal
focal plain
plain of
of
totothe
laserlight.
light. The
Theemittance
emittance growth
growth is
is given
given for
for
laser
twodifferent
differentlaser
laserpowers,
powers, 30
30 GW
GW -bottom
–bottom
two
curve;800
800 GW
curve;
GW–- top
topcurves.
curves.
-1
-0.5
-0.50 00.5 0.5 1
length, m
J
11.5 1.5
FIGURE 4. An example of beta-function,
= Px
βTX
βTy
Tx =
y>, behavior in the LACARA magnet
With magnetic
magnetic field
field required
required to
to maintain
maintain the
the resonance
resonance conditions,
conditions, the
With
the Brillouin
Brillouin
radius equals
equals to
to 44 jim
at full
full current,
current, and
and 1.2
µm at
radius
1.2 µm
jim if
if the
the emittance
emittance filter
filter isis
implemented. When
When 800
800 GW
GW laser
laser power
power is
is applied,
applied, the
the minimal
minimal electron
implemented.
electron beam
beam
356
waist is 35 jim (28 jim with the emittance filter); thus, the space charge effects can
be fully neglected.
PRESENT STATUS
The LACARA will operate at the ATF experimental floor, second beam line. The
detailed layout of the experiment is below (Fig. 5)
Electron bunches from the ATF RF linac enter the LACARA experiment via a
bending dipole magnet at the left.
Between this dipole and the LACARA solenoid three quadrupole magnets (quads)
are placed to focus the electron beam to the required transverse sizes. For the
present experiment the required beta function at the matching point between the
beam line and the solenoid entrance has to be PTO = PI* = Pxy ~ 0.68 m (- 40 % -s+90 %), while 3px/ 9s = 0. The last quad in the focusing series is movable. Together
with current adjustment in all three quads, one will be able to change PTO from 0.14
to 1.8 m. In order to keep the dispersion function Dx equal to zero one will need also
to adjust slightly the current in the first five quads located before the dipole (not
shown in the layout). The behavior of both beta functions are plotted in Fig. 6
The second quads assembly, located after the LACARA solenoid, has the purpose
of tightly focusing the accelerated electron beam prior to its passing through the
second bending dipole. Both assemblies are mounted on double continuously
supported rail tables with adjustable carriages. The design will provide quad
alignment along a given line with precision of around 25 jim. Residual alignment
errors are eliminated by means of trimmers.
The solenoid provides a uniform guiding magnetic field up to 6 T at 77 amps over
the length of 1.6 m. The unit's flange-to-flange length is 2343.4 mm. Its windings
have operational temperature of 4.2 K°, and are chilled by Sumitomo SRDK-408
cryocooler head through a thermally conductive mount. The total time for cooling
down from the room temperature is about two days. This magnet was constructed at
the Everson Electric Co., Bethlehem. PA.
The magnet axis can be found by means of a stretched wire technique with a
precision better than 25|im. However, when the wire position is referred to external
fiducials, the precision will be no better than 150|im. Fortunately, there is a way to
improve upon that. The center of misalignment of the electron beam plots a
quasiperiodic curve with a period of 0.582T in the plane orthogonal to the beam. By
gathering this information at several positions of the solenoid, one should be able to
position the magnetic axis with a precision of 3-4|im with respect to the electron
beam.
A special table, positioned precisely with four degrees of freedom, is used to
support the magnet. It has been built recently at Yale Physics Department Shop.
The accuracies of positioning under appropriate load are: yaw - 2.66 jiirad/ motor
step; pitch -1.44 /urad/ motor step; lateral shift -1.56 /urn/ motor step; vertical shift
-10 urn, non motorized.
357
LACARA at
ATF
(LAser Cyclotron Auto—Resonance Accelerator)
^
FIGURE 5. LACARA at ATF, second beam line
There are three prime locations for beam monitors. Each monitor (BPM) is a
retractable OFHC mirror mounted on an actuator stroke. Tilted by the angle of 45°
to the beam line it reflects the transition radiation produced by an oncoming electron
bunch toward a monitoring CCD (visible spectra). It has been recently shown at
ATF that this approach provides the most reliable measurement of beam sizes for
waists not exceeding 100 - 200 jim [9]. There are beam splitters inserted into the
light paths, separating visible radiation from IR. The CC>2 laser rays, which are also
reflected by mirrors, are separated from the visible light by these beam splitters and
propagate towards pyroviewers. Thus, both the electron and laser beams are
monitored simultaneously at each given location. After each retraction the new
position of the beam monitor screen will be referred to a reference axis.
To establish the reference axis a HeNe laser located outside of the vacuum is
employed. The unit introducing this light into the system is similar in design to the
beam monitor. However, instead of using a simple stroke actuator it uses in addition
an adjoined kinematic base having reproducibility ~1 jirad. For the light initial space
and angular adjustment, the HeNe laser is mounted on the top of an accurately
positioned stage having five degrees of freedom. The HeNe laser will be used as the
reference axis not only when the experiment is operated, but during equipment
installation too.
A new magnetic spectrometer will be required to measure the energy difference
between the unaccelerated bunch and the accelerated bunch, and is being currently
developed.
358
•\
DISTANCES in MM
The loe-ta-function before -the solenoid
p = 0,14 - 1,8 n is achivable,
0 = 0.14 - 1.8 n is achivable
Q1,Q2,Q3 - quadripoles
Ql,Q2,Q3-quadrupoles
FIGURE 6. The beta function behavior before the LACARA solenoid, - two examples for the
different quadrupoles currents and also two different positions of the third quad are shown.
The simulation is made by the MAD-code, version 8.51/07. [8]
The laser transport system uses a single lens with R = 12m to focus the CC>2 laser
light in the middle of the solenoid. The particular waist (31.1 mm) is required at the
lens location, and is provided by the means of ATF telescopic system (not shown in
Fig. 5). All mirrors are plain and serve only to direct the light. High precision
mounts are used to achieve adequate positioning. There is a vacuum-sealed ZnSe
coated window that introduces light into the vacuum, and is subjected to more
radiation load than other elements. The upper energy threshold is about:
Ptot' &t[Joules] = (wwin[mm]/ll.3)2 = 6.72 J
(14)
where Wwin is the waist at the window location.
A laser dump is used at the end of experimental line. The design uses a
spherical mirror reflecting light by 90° toward a NaCl window, which separates the
vacuum and air-pressurized volumes of the dump. The wave front after reflection is
a generalized spherical surface having major radius twice larger than that of the
minor. The design has very compact dimensions, yet it has the upper energy
threshold around 6.83 J, and dumps more than 95 % of the incident power outside
the vacuum chamber.
Future plans for this facility include the generation of fsec-duration bunches
[2].
359
ACKNOWLEDGMENTS
The authors acknowledge helpful discussion with the ATF staff: Ilan BenZvi, Marcus A. Babzien, Marty Woodle, Igor Pogorelsky, Vitaly Yakimenko, Xijie
Wang, and the financial support of the DoE.
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