Plasma Source Design for the PWFA Experiments
at SLAC
K. A. Marsh
University of California, Los Angeles CA 90095
P. Muggli
University of Southern California, Los Angeles, CA, 90089
Abstract. We discuss the design issues associated with producing a plasma source for the plasma
wake field accelerator (PWFA) experiments at SLAC. There are many possible sources, but for our
purposes uv, single photon ionized, lithium vapor, in a heat pipe oven, is our best option. Optimum
parameters are derived and the plasma decay rate is estimated.
INTRODUCTION
There have been several ideas proposed for a plasma source for the E-164, PWFA
experiments at SLAC. These include uv single photon ionized metal vapors, multiphoton
ionized metal vapors, and capillary discharges. Also, ionization by the electron beam
itself is promising in some cases. All the plasma based accelerator schemes require meter
scale length, high density,~1014 to ~1017 cm"3, uniform plasmas. All of these plasma
sources have their advantages and disadvantages, depending on the plasma accelerator
requirements.
Since we have looked at uv single photon ionized metal vapors in detail we will
discuss some of the relevant design issues here. We will not discuss capillary discharges
in this paper because much is already contained in these proceedings. Multiphoton fully
ionized plasmas could potentially be very uniform, however maintaining the required
high laser fluence over meter scale lengths is not yet practical for our purposes.
Ionization induced laser refraction is also a problem when trying to use lasers to produce
long scale length plasmas. Since tunneling ionization by the electron beam looks
promising, we will mention it here and discuss the details in another paper in these
proceedings.
SINGLE PHOTON IONIZATION OF METAL VAPORS
For the purpose of the E-157 and E-162 experiments, a heat pipe oven of 1.4 meters of
lithium vapor was partially ionized using an ArF excimer laser. The resulting plasma
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
614
was nearly uniform and densities up to 3xl014 cm"3 were achieved. Since the plasma was
formed by single photon ionization, the plasma density was proportional to the laser
fluence (joules/cm2) and the uniformity of the plasma was determined mainly by the
uniformity of the laser profile. The maximum plasma density we could produce was
limited by the laser fluence. For the E-164 experiment, we would like to achieve uniform
plasmas with densities of 5xl015 cm"3 or greater and about 30 to 40 cm long.
The tables below list some of the properties of the metal vapors we have considered.
Table 1 shows the ionization potential for the vapors in eV and the photo ionization cross
sections for three uv laser wavelengths given in cm2. The ArF excimer laser wavelength
is 193 nm and the photon energy is 6.42 eV. The KrF laser wavelength is 248 nm or 5.0
eV. The frequency quadrupled YAG wavelength is 266 nm or 4.66 eV. Lithium vapor
has the largest cross section, and therefore is most efficiently uv laser ionized. An ArF
laser is needed to ionize lithium.
TABLE 1. UV ionization cross sections of some metal vapors.
Vapor
Ionization eV
a at 193 nm
a at 248 nm
Li
5.392
NA
1.8xlO"18
NA
Na
<10"20
5.139
K
4.341
1.7xlO"19
1.3xlO"20
20
Rb
4.177
5xlO"
IxlO"20
19
3.894
Cs
1.6xlO"
7xlO"19
a at 266 nm
NA
NA
2xlO"21
2xlO"20
6xlO"20
There are other concerns with regard to the selection of the vapor. The beam can
ionize the vapor by impact ionization. Bruhwiler has a good review and a calculation of
the impact ionization cross section in PRST-AB, vol. 4 Oct. 2001 pg. 101302. Bruhwiler
also looked at impact ionization effects in the working group. The impact ionization
cross section increases with atomic number and so impact ionization of heavier metal
vapors might cause a problem when interpreting experimental results due to changes in
the initial plasma density. The impact ionized electrons can be trapped by the large
amplitude plasma wake causing beam loading and reducing energy gain. Impact
ionization effects can be reduced by keeping the vapor density as low as possible, and
producing a high ionization fraction. Ideally, the plasma should be fully ionized.
The second table shows the oven temperature required to produce a vapor pressure of
1 Torr and 10 Torr for the vapors listed. Also shown is the A coefficient. The A
coefficient is a figure of merit with respect to heat pipe oven vapor homogeneity. It is
described in [C. R. Vidal, J. Appl. Phys., Vol. 44, No. 5. May 1973, pg. 2225]. The
smaller A, the more homogeneous the vapor column. Heat pipe ovens with higher atomic
number vapors are more uniform and can be operated at relatively lower temperatures.
However, concerns about impact ionization problems lead us to choose lithium.
615
TABLE 2. Thermal properties of metal vapors.
Vapor
Li
Na
K
Rb
Cs
Atomic Mass
6.94
23
39.1
85.5
133
Temp. @ IT and 10T
1013, UTOdeg.K
710, 817
612, 709
562, 652
545, 634
A coef. @ IT and 10T
.133, .0253
.0708, .0137
.0546, .0114
TBD
.0715, .015
SINGLE PHOTON PARTIALLY IONIZED VAPOR
For a single photon ionization, as the laser propagates through the vapor it is absorbed
according to, w=w0Exp[-n0az], where w0 is the laser fluence in joules/cm2 in vacuum, r^
is the neutral vapor density, a is the photo ionization cross section and z is the
propagation distance. Since each photon absorbed produces an electron, the plasma
density, ne is given by, ne=no(l-Exp[-wa/hv]) where hv is the laser photon energy in
joules. Absorption of the laser as it propagates will cause the plasma density to drop
along z. To keep the plasma density axially uniform, the laser must be focused through
the vapor to compensate for absorption.
Using the above equations, a plot of the plasma density versus n0 for Li, Cs and Rb,
vapor is shown in Figure 1. The curve for Li is on the left, Cs is the middle curve, and Rb
is on the right.
10
no (10*16)
20
Figure 1. Plots of uniform plasma density (cm"3) versus neutral vapor density, n0, for Li, Cs, and Rb vapor
using an ArF laser at 193 nm. The curve for Li is on the left, Cs is the middle curve, and Rb is on the right.
The plot shows that for any uniformly partially ionized vapor that maximum density, r^ is independent of
the vapor ionization cross section and there is an optimum neutral density. Lithium has the highest
ionization fraction.
616
The vapor length was 30 cm long and the laser parameters were the same in each case
shown. The laser wavelength was 193 rim, and focused to produce a fluence of 300
mJ/cm2 in vacuum at the end of the oven. The laser fluence in the vapor was kept
constant along z, to give an axially uniform density plasma. As the plots show, the
maximum achievable uniform plasma density is the same for all vapors, but the
ionization fraction is larger for larger a. There is an optimum n0 to produce the
maximum uniform plasma density. The curves in Figure 1 can be understood for
wa/hv«l. Then, ne~n0wa/hv~n0w0Exp[-n0aL] a/hv at z equals the oven length L.
For partially ionized, maximum density, axially uniform, plasma, the optimum neutral
density is n0=l/aL. Therefore, in order to maintain the maximum axially uniform density,
the laser needs to be focused through the length of the vapor such that the fluence
increases by Exp[l] or 2.7 times. The maximum uniform plasma density is
n
e,max = wQExp[-l]/hvL, which does not depend on a. Also, noaL=l, therefore a shorter
vapor would have a proportionally higher maximum density. The maximum integrated
density length product is nemaxL = w0Exp[-l]/ hv, which for a given laser wavelength
depends only on the laser fluence. If we want ne maxL to be as large as possible, there is no
substitute for laser fluence. The ionization fraction at maximum uniform plasma density,
is ne, max/Ho = w0Exp[-l]a/hv. The ionization fraction of Li in Figure 1 is ~17% and for Cs
is 1.7%.
IONIZATION INDUCED REFRACTION
As the laser propagates through the vapor and produces plasma, the plasma will act as
a negative lens causing the laser to defocus. This in turn will reduce the ionization rate
and make it difficult to maintain the desired plasma density and homogeneity. The laser
beam will begin to defocus when n^ > A/zR, where r^ is the plasma density,
nc=(c/5l9000)2 is the critical density at the laser wavelength 5l and ZR is the laser Rayleigh
length. For ^=193 nm and ne=lx!016 cm"3, the maximum ZR ~ 55 cm. This imposes a
limit on the plasma length and density of laser ionized plasma sources for PWFA.
LIMITATION ON TOTAL ENERGY GAIN FOR A SINGLE
PHOTON IONIZED PLASMA
With a single photon ionized plasma source there is a limit to how much energy gain
we can obtain for a given laser fluence based on linear PWFA theory. From the linear
theory, the optimum density for a given bunch length is given by kpGz=V2 and so
ne~l/az2. The optimal gradient depends only on the bunch length and charge according to
the relation, Gradient-Nya/ where Nc is the beam charge. As shown above, neL is fixed
by the laser fluence (neL-w). Therefore, the bunch length fixes ne, and L is not a free
parameter. The total energy gain is, (Gradient)(L) ~Nc/az2L~Ncw. The implication of
this is the total energy gain is fixed by the laser fluence and beam charge.
We plan to have a plasma source where we can trade plasma density for plasma length
and so make adjustments for whatever bunch length is finally used in the experiment.
617
PLASMA RECOMBINATION
Once the laser pulse forms the plasma, the plasma will decay rapidly, mainly due to
three-body recombination. The time dependent plasma density with ionization and
recombination is given by,
dn
—ft = dt
a = ne 8.75xlO~27T;45cm3 /sec
(1)
(2)
where a is the three-body recombination rate. The plasma electron temperature Te is in
eV and ne is the density in cm"3. A calculation of plasma recombination is complicated by
the fact that a, has a strong dependence on electron temperature which goes as Te"45. For
the case of lithium vapor ionized by a ArF laser the plasma electrons have an initial
excess ionization energy of -1 eV. and rapidly cool to the vapor temperature which is
about .1 eV. The plasma cooling equation is given by,
dTe
= v(T i -T c )
dt
(3)
(4)
where ml9 nI? and T{ are the ion mass, density, and temperature respectively. A is the
Coulomb logarithm. The electron temperature and density are coupled through the above
equations. The three-body recombination rate also depends on the square of the plasma
density and so higher density plasmas recombine more rapidly. The equations were taken
from the NRL Plasma Formulary and plotted using Mathematica.
Ov2
to
fo
100
Figure 2. The theoretical plasma formation and recombination for a uv ionized lithium plasma formed by
single photon ionization using an ArF laser pulse with a 20 nsec FWHM. The right plot shows the
theoretical cooling time, Eqn. (3). The initial plasma density is 1016 cm"3 and the initial temperature is
assumed to be the excess ionization energy, 1 eV.
618
The results for a 1016 cm"3 lithium plasma, ionized by a 20 ns long ArF laser pulse, are
shown in Figure 2. From Figure 2 the plasma density is nearly constant for about 15 ns
and then rapidly decreases. Experimental studies of plasma recombination for cold high
density plasma show that the decay time is slower than that predicted by theory. (See O.
L. Landen PRA vol. 32 no. 5 Nov. 1985 pg. 2972). Hopefully the plasma will not decay
too rapidly for our experimental goals. To maintain the same shot to shot plasma density,
accurate synchronization and monitoring of the timing will be needed. We also are trying
to develop time resolved spectroscopic plasma density diagnostics which will allow
density measurements on a shot to shot basis.
TUNNEL IONIZATION BY THE ELECTRON BEAM
When the space charge electric field of the beam approaches the binding potential of
the neutral gas atoms, tunneling or field ionization will occur. Under the right conditions,
tunneling ionization can be used to create fully ionized plasma. This would allow us to
produce much longer plasmas at much higher densities than laser produced plasmas. The
possibility of using tunneling ionization to create the plasma for the E-164 experiments
was discussed in our working group. Atomic vapors with a low ionization potential such
as cesium is easily ionized by electron bunches with a radial rms size of 20 Jim and
longitudinal rms size of 100 Jim. We discuss the calculations and apply them for possible
PWFA experiments at SLAC in these proceedings.
ACKNOWLEDGEMENTS
We gratefully acknowledge our E-164 collaborators and members of the Beam Driven
Accelerator Working Group and our DOE and NSF support. Work supported by DOE
grants, DE-FG03-92ER40727 and DE-FG03-92ER40745 and NSF grant, PHY-0078715.
619