PROPOSAL
TO
USER’S COMMITTEE, CENTER FOR ACCELERATOR PHYSICS
BROOKHAVEN NATIONAL LABORATORY
from
Omega-P, Inc.,
Beam Physics Laboratory,
J.
L. Hirshfield, principal investigator
tel: (203) 432-5428
fax: (203) 432-6926
e-mail: jay.hirshfield@yale.edu
LASER-DRIVEN
CYCLOTRON
AUTORESONANCE
ACCELERATOR
LACARA
INTRODUCTION
Omega-P, Inc. has carried out analytical
and computational studies of a novel accelerator-driven electron acceleration
mechanism LACARA, with support in
1999-2000 under a SBIR Phase I grant from High Energy Division, Department
of Energy. This study led to a Phase
II proposal to DoE, currently pending, to support a proof-of-principal experiment
at Brookhaven National Laboratory Accelerator Test Facility. Obviously, acceptance of this proposal by the
ATF User’s Committee is also required. This
document is intended to provide background information to enable the Committee
to reach a considered judgement on this project. Included here are excerpts from the Phase II
proposal submitted to DoE.* Further
information will be available, as needed, during a verbal presentation scheduled
to be given to the Committee during its forthcoming meeting June 1-2, 2000.
*It
is expected that a decision from DoE on Phase II support for this project
could be announced prior to the June 1-2 User’s Committee meeting. If that decision is not positive, Omega-P, Inc.
will withdraw this proposal to ATF.
SIGNIFICANCE AND BACKGROUND INFORMATION,
AND TECHNICAL APPROACH
Under Topic 11a in the 1999 SBIR Program Solicitation entitled
Advanced Concepts and Technology for
High Energy Accelerators—New Concepts for Acceleration, grant applications
were sought to develop new or improved acceleration concepts to provide very
high gradient (>100 MeV/m for electrons) acceleration of intense bunches
of particles. Omega-P, Inc. submits
this proposal in response, describing Phase II of a three-phase program to
develop a laser-driven cyclotron autoresonance accelerator (LACARA).
The analysis carried out during Phase I confirms that LACARA (a) can provide an acceleration gradient in one stage of the order
of 100 MeV/m, (b) can accelerate
continuously along a 150-cm length in vacuum using an available laser, and
(c) can accelerate in a vacuum with good
uniformity all electrons within a millimeter-length bunch.* The Phase I analysis has been applied to the
experimental parameters available at Brookhaven National Laboratory Accelerator
Test Facility (BNL-ATF), where experiments to confirm the analysis using a
prototype LACARA are proposed for
Phase II.
Electron acceleration using intense lasers has engendered
significant attention within the accelerator research community. This interest stems from the enormous optical
electrical field strengths
that can be obtained with a focused
laser, i.e. of the order of
TV/m, where the intensity
is in
. Since compact terawatt focused lasers
can have
, field strengths of the order of TV/m are possible. Of course, since this field is transversely
polarized, it cannot give much net acceleration to a charged particle directly,
so an indirect means must be employed to achieve net acceleration. The basis upon which LACARA rests is cyclotron resonance, using an axial static magnetic
field. The magnetic field can be adjusted
to allow transverse deflections of electrons that move along a helical path
to be synchronous with the rotating transverse electric field of a circularly-polarized
laser beam, thereby allowing the field to do work on the electrons.
LACARA is a laser-driven
accelerator that operates in vacuum. It does not require a pre-bunched beam; nevertheless
all injected electrons can enjoy nearly the same acceleration history.
LACARA is operated without a tight laser focus, so the Rayleigh length
can be 10¢s of cm for a 10.6
laser wavelength, and continuous acceleration in vacuum over several Rayleigh
lengths can take place. Phase bunching—but
not spatial bunching—occurs in LACARA, which explains how all injected electrons can experience nearly
the same accelerating fields, since circularly-polarized laser radiation is
used. Furthermore, the effective group
velocity in LACARA exceeds the particle’s
axial velocity, so operation with strong pump depletion is possible without
causing undue energy spread for the accelerated beam. It is shown that LACARA is not limited to being a
“
-doubler” (as is its microwave counterpart
CARA), because the relativistic energy factor
____________.
*The preliminary analysis underlying
LACARA is presented in a forthcoming
publication entitled “Laser-driven cyclotron autoresonance accelerator with
production of an optically-chopped electron beam,” by J. L. Hirshfield and
Changbiao Wang, Phys. Rev. E 61, June 2000 (to be published and appended
herein.)
can be increased
by more than a factor-of-two in a single stage. This is because stalling of the electron beam
in the axial magnetic field can be avoided. (In this expression,
is the electron rest energy plus kinetic
energy, and
is the rest energy.) Another feature
of LACARA is the relatively low
level of magnetic field required for the cyclotron resonance interaction when
a
laser is employed.
For the prototype LACARA demonstration proposed here for
operation at BNL-ATF, the magnetic field required is only 6 T, a field that
can be obtained using a cryogen-free superconducting magnet system available
from a number of industrial vendors.
During Phase I, efforts were directed towards a detailed
study of LACARA, using computational
tools available to Omega-P, Inc. The
main goal is to develop a design for the prototype LACARA based on parameters of experimental facilities available at
BNL-ATF, including an rf linac to provide a 50 MeV beam to be accelerated,
and a high-power
-laser to drive the acceleration. It is necessary in Phase II for Omega-P to procure
a high-field solenoid magnet, specifications for which evolved during the
Phase I study. Some compromise in specifying
the parameters of the magnet is necessary on account of budgetary limitations,
but this is not expected to prevent confirmation of the underlying principles
of LACARA, and for quantitative
comparison between performance and theoretical predictions. A presentation by Omega-P is scheduled for
June 1-2, 2000 before the BNL-ATF Steering Committee, to request approval
for the installation and test of a prototype LACARA,
contingent upon approval by DoE of the Phase II project. A letter from Dr. Ilan Ben-Zvi, Head of ATF,
expressing strong interest in LACARA,
is enclosed in this proposal.
ANTICIPATED
BENEFITS
The
physics underlying laser-based acceleration provides a wide range of fertile
problems that continue to motivate a not-insignificant number of research
workers. Still, none of the schemes
for acceleration under study has yet produced a beam with low enough energy
spread and emittance to be considered suitable as one stage out of many in
a machine for nuclear or high energy physics experiments, even assuming that
multi-stage operation is perfected. A
single stage should be capable of uniformly accelerating a bunch containing
a significant number of electrons (1 nC, for example), with a gradient of
the order of 100 MeV/m, and producing a beam with an acceptable emittance
(<5 mm-mrad, for example). These
attributes are anticipated for LACARA. Efficiency is an oft-overlooked but critical
parameter, since the energy per pulse that will be available in a laser beam
is not unlimited. For example, for
a 1 Joule laser pulse, energy conservation sets a limit of 100 MeV that can
be gained by
electrons per pulse, corresponding
to
nC, where
is the efficiency with which laser
energy is imparted to the electrons. For
, only 10 pC can be accelerated; however, for
, as is shown below to be possible in LACARA, over 5 nC can be accelerated. This is a critical issue, since energy consumption
by an eventual high energy accelerator with acceptable luminosity dictates
that a reasonable level of efficiency for the driver is a sine qua non. Additional potential advantages of LACARA, as compared with other laser-based
accelerator schemes, include the absence of any material medium in or nearby
the accelerating region. In some vacuum
accelerator schemes, nearby mirrors with apertures or surfaces that support
surface waves are required. It has
been shown that these surfaces can suffer permanent damage within a short
time when illuminated by intense lasers. Or,
when solid dielectric loading is used to provide for wave slowing, breakdown
limits in the dielectric will limit the acceleration gradients. And in the inverse Cerenkov laser, where a low-pressure
gas fill is used to provide the wave slowing, a small degree of ionization
of the gas could be sufficient to cause a significant change in the index
of refraction of the medium; this leads to loss of synchronism between the
radiation and the accelerated electrons. This
recitation of concerns, already thoroughly discussed in the literature, is
not meant to imply that such problems cannot be overcome; rather it is to
draw attention to issues that are not inherent to a vacuum accelerator such
as LACARA.
These
advantages for LACARA may thus provide
a basis for electron and positron accelerators using powerful lasers, to be
designed and built to take advantage of the high electric fields lasers provide,
to generate an accelerated beam with a small energy spread and low emittance,
and to transfer laser pulse energy to the beam with high efficiency.
Laboratory proof of these virtues in the SBIR Phase II project proposed
here by Omega-P could open the door towards realizing a high-gradient electron/positron
accelerator free of many irksome features of other laser-based schemes. The potential market for the large number of
magnets and optical stages of LACARA needed to provide a beam of interest
to the high energy physics community is very large indeed, and represents
a highly attractive future business opportunity.
DEGREE
TO WHICH PHASE I HAS DEMONSTRATED
TECHNICAL
FEASIBILITY
The overall goals of the Phase I program include these general objectives:
·
refinement of the theory and computations that underlie LACARA;
·
analysis of LACARA performance
for a range of experimental parameters;
·
determination, through consultations with Brookhaven ATF personnel, of
a range of parameters that could be available for a proof-of-principle test
of LACARA;
·
consultations with vendors, to define specifications and cost for a cryomagnet
designed to meet the needs of the proof-of-principle LACARA, and to fit within the ATF experimental
hall;
·
design of the LACARA proof-of-principle
apparatus to be built during Phase II; and
·
obtaining approval from the ATF Steering Committee for a Phase II proof-of-principal
test of LACARA, contingent upon
approval by DoE of the SBIR Phase II program.
Detailed discussion of tasks undertaken to pursue each of
these goals is given below. But before
elaborating on these tasks, performance for the prototype LACARA that is proposed for construction and evaluation during Phase
II is first summarized. A sketch of
LACARA is shown in Fig. 1. Copper mirrors direct a laser beam to pass along
the axis of a 6 T solenoidal magnetic field set up by the surrounding cryomagnet.
For this prototype, the
10.6 mm CO2 laser power
is taken to be 2 TW,* the minimum laser spot radius is taken to be
1.0 mm, with a Rayleigh length
29.6 cm. The electron beam and the
laser radiation interact over a length of
178 cm, but the uniform portion of the magnetic field only extends for about
150 cm. The (nominal) 1 A, 50 MeV beam
injected at z = 0 has a normalized
emittance of 2.0 mm-mrad.** Compromises
were made in selecting these parameters to be the basis for design of the
prototype LACARA, mainly on account
of the high cost of a magnet with a more suitable field profile.
The mirror spacing is 225 cm, and the 8-cm i.d. coil length of 180
cm provides a nearly uniform field region of 150 cm in length.
Electron orbits are computed from one mirror to the other, all through
the fringing fields at the ends of the coil.
Fig. 1. Sketch of LACARA
prototype, not to scale. Accelerating charge bunch is shown at center.
Fig. 2 shows, with the solid lines, the magnetic field profile
and the average relativistic energy
factor
as they vary along the axis of LACARA.
Using dashed lines, the same quantities are shown
for the ideal resonance magnetic field profile. Table I compares results for the actual and
ideal magnetic field profiles.
_____________.
*The design output power for
the ATF CO2 laser is 3 TW. (I.
Ben-Zvi, private communication).
**I. Ben-Zvi, private communication.
Fig. 2. Energy gain and magnetic field profile for the
prototype LACARA (solid lines).
Dashed lines show these parameters for the idealized resonant magnetic
field profile.
| |
one-coil B-field profile |
ideal B-field profile |
| final beam energy |
120.9 MeV |
135.5 MeV |
| average accel. gradient |
47.2 MeV/m |
57.0 MeV/m |
| maximum accel. gradient |
75.7 MeV/m |
100.6 MeV/ |
Table I. Comparison of LACARA performance for the proposed affordable one-coil magnet system
with that for the ideal resonant magnetic field profile.
These results for a LACARA
prototype employing an affordable magnet are seen to extract some sacrifice
in achievable acceleration, but not so severe a sacrifice to prevent a careful
comparison to be made between prototype performance and predictions of the
theory. It might even be argued that,
until full confidence is established in the viability of LACARA based on laboratory results, investment in a more sophisticated
magnet system might not even be warranted. Moreover, the (nominal) 6 T, 150-cm long uniform
region, 36-mm room-temperature bore, non-cryogen, superconducting magnet that
Omega-P proposes to acquire for the prototype LACARA is a versatile laboratory instrument that can find other applications
in the future. This might not be so
for a magnet with a more specialized field profile.
Tasks for achieving the Phase I goals listed above are described
in the Phase I proposal, which is enclosed herein. The title of each task is given in bold italics
below, together with details of the results obtained during Phase I.
Task A: Include finite emittance and energy spread
for the injected beam in computations.
Since examples given in the Phase I proposal were for an initially
cold beam, it is important to judge how a finite initial transverse beam emittance
can affect LACARA performance. In carrying out this task, acceleration was
computed for finite initial transverse emittance, and for several initial
beam energies to simulate the influence of a finite energy spread. The normalized transverse emittance for the
BNL-ATF beam that is to be used with the prototype LACARA experiment is
= 2.0 mm-mrad [mm].
At 50 MeV, this implies a rms emittance of
0.0202 mm-mrad. For the simulations described below, it was
more convenient to specify initial beam coordinates and momenta using the
phase-space transverse “98% emittances”
and
, which are here defined by the area in
and
phase space within which
98.2% of the particles are found.
For a beam having Gaussian distributions of coordinates and momenta,
and with
0.0202 mm-mrad, it was found that
=
= 0.125p mm-mrad. In the examples shown in this section, laser
parameters were as in the example of Fig. 2.
For some of the examples shown in this section, the magnetic field
profile shown in Fig. 2 (the “one-coil profile”) was employed.
For other examples a profile that is closer to the ideal resonant profile
(the “two-coil profile”) was employed; the two-coil profile is shown in Fig.
3. From this figure, it is seen that
final beam energy, and average and maximum acceleration gradients achievable
with the two-coil profile are 128.0 MeV, 52.0 MeV/m, and 87.7 MeV/m.
Fig. 3. Energy gain and magnetic field profile for a
LACARA using the two-coil magnet (solid
lines). Dashed lines show these parameters
for the resonant magnetic field profile.
It is important to note a significant
difference in the model used for the one- and two-coil examples, and that
for the resonance profile. It is taken
in the computations that the beam for the one- and two-coil cases enters and
exits the laser interaction region between the mirrors by moving along the
full fringing magnetic fields at the edges of the magnet coils. However, in computations for the resonance profile,
the interaction only occurs between 50 and 200 cm, as shown by the dashed
lines in Fig. 3. In practice, this
could be arranged in the laboratory by positioning two mirrors in the magnet
bore to deflect the laser beam in and out of the beam path once the coil field
reached the resonance value. To accomplish
this in practice would require a cryomagnet of larger room temperature bore
diameter than the 36-mm for the one-coil affordable system to be used in the
LACARA prototype.
Fig. 4 shows, for the two-coil profile, and for fixed value
of
= 0.125p mm-mrad, the relativistic energy
factor reached during acceleration, for various values of initial electron
beam radius
. Smaller
implies a larger range of initial transverse
momentum that leads to loss of phase synchronism during acceleration, with
a concomitant decrease in final achievable energy. Larger
allows peripheral electron orbits to
move out of the intense core of the laser spot, and thereby to achieve a lower
net acceleration. The optimum value
of initial beam radius found is
= 0.3 mm, for which the final average
beam energy is 128.0 MeV.
Fig. 4. Achievable final average beam energy factors
using the two-coil profile, for three values of initial beam radius
, with fixed initial emittance
= 0.125p mm-mrad.
Fig. 5 shows the acceleration history near the end of LACARA for different initial beam energies
that are 1% above and below the design energy of 50.0 MeV; for all cases
= 0.125p mm-mrad. As
is seen, the final beam energy variation is less than ±1%. This
strongly suggests that, for a beam with initial energy spread within ±1%, that the acceleration will
be essentially the same as for a mono-energetic beam.
Fig.
5. Average beam energy for values of
initial beam energy that are 1% above and below the design energy of 50.0
MeV.
The effect of varying the initial transverse emittance was computed,
with results shown in Fig. 6. Here,
for the two-coil magnetic field profile, and for
= 0.30 mm, results are shown for
=
= 0.125p mm-mrad (case 1), 0.175p mm-mrad (case 2), and 0.225p mm-mrad (case 3). As is evident, substantial decrease in achievable
final beam energy ensues as the initial
Fig. 6. Acceleration in LACARA for three different initial beam emittances.
beam
emittance increases. It is likely that
a somewhat greater final beam energy could be realized in the higher emittance
cases by optimization of the initial beam radius in each case. Nevertheless, the lesson taught in this example
is the necessity for employing a beam of reasonably small initial emittance
in order to realize the full potential of LACARA.
The evolution of transverse emittance
during acceleration in LACARA has
also been examined. This is an unusual
situation to evaluate, since the beam executes an orderly gyration about which
random variations in coordinates and momenta occur, the latter arising from
random variations in the initial values. The orderly variations can be described by “geometric”
emittances, defined as
, and
, where
are orderly deviations in the respective
variables, quantities that are normally zero for solid laminar beam.
Geometric emittances in LACARA presumably can be made to approach
zero using a sequence of quadrupole lenses. (This point is discussed in sub-section E below.) Figs. 7 and 8 illustrate both the orderly and
random nature of the beam, wherein plots in
and
phase space are shown for an ensemble
of 1889 particles that are injected at four equally-spaced intervals during
one optical cycle (35 fs). In this
exercise, the resonance magnetic field profile was chosen.
Fig. 7. Phase space
(a) at z = 0, (b) at z = L/2,
and (c) at z = L.
Fig. 8. Phase space
(a) at z
= 0, (b) at z = L/2, and (c) at z = L.
The
phase-space plots are shown at the point of injection (z = 0), at a point mid-way along LACARA (z =
= 74.1 cm = L/2), and at the end of LACARA (z =
= 148.2 cm = L). Variations
in arrival times
and
at z = L/2
and z = L for groups of particles that departed at the same time are seen,
due to slightly differing histories of axial velocity. These variations are of the order of 4-5 fsec
out of
fs (at z = L/2) and 7-8 fs out of
fs (at z = L). The variations are fractionally tiny, but still
amount to a significant fraction of the optical period (35 fs). From the phase space plots, one can estimate
that
(0.4)(5)p
= 2p mm-mrad, and similarly
for
. However, the random variations, evaluated
at fixed arrival time at z = L, give maximum values
(0.3)(0.5)p
mm-mrad, only slightly larger than the initial transverse areal emittances.
In any case, the method of estimation isn’t accurate enough to distinguish
the initial and final values. Thus,
to the extent that geometrical emittance can be manipulated and reduced using
quadrupole lenses, it appears that emittance growth—as it is usually described—is
not in principle a serious issue in LACARA,
when the resonance magnetic field profile is used.
Task B: Examine effects of errors i