Proceedings of International Conference on Physics in ... - KEK

REACHING THE SCHWINGER LIMIT WITH X-RAYS*
Charles K. Rhodes, John Boguta, Alex B. Borisov, Shahab F. Khan, James W. Longworth, John C.
McCorkindale, Sankar Poopalasingam, Ervin Racz # and Ji Zhao
Laboratory for X-ray Microimaging and Bioinformatics, Department <strong>of</strong> Physics, University <strong>of</strong>
Illinois at Chicago, Chicago, IL 60607-7059, USA
Abstract
The derivation <strong>of</strong> an elementary figure <strong>of</strong> merit shows
that attainment <strong>of</strong> an intensity corresponding to the
Schwinger/Heisenberg Limit (~ 4.6 x 10 29 W/cm 2 ) is
significantly facilitated by the use <strong>of</strong> coherent x-ray
sources in the kiloelectronvolt regime. For the Xe(L)
system at ~ 4.5 keV, a minimum pulse energy <strong>of</strong> ~ 1.5 J
and corresponding peak power P0 ~ 300 PW are estimated.
INTRODUCTION
The history <strong>of</strong> high-intensity nonlinear interactions, that
commenced in 1961 with the observation <strong>of</strong> second
harmonic radiation [1] at 347.2 nm in crystalline quartz,
spans a range <strong>of</strong> ~ 10 18 in experimental intensity and
remains a stable, robust province <strong>of</strong> laser-based research
after a half century. The generation <strong>of</strong> focal intensities in
the 10 20 -10 21 W/cm 2 range is presently a routine
achievement. Over a period <strong>of</strong> ~ 25 years, a path <strong>of</strong>
research was cut through this field <strong>of</strong> nonlinear
phenomena that led to the development <strong>of</strong> a multikilovolt
(~ 4.5 keV) x-ray amplifier <strong>of</strong> exceptional peak brightness
[2-5] that is excited by femtosecond KrF* (248 nm)
pulses and whose experimentally based power scaling
limit for a compact laboratory instrument falls in the
multipetawatt realm [6]. The existence <strong>of</strong> advanced highenergy
KrF* technology [7], that has been independently
developed for fusion applications, could be readily
adapted to extend the coherent x-ray power level into the
200 - 500 PW regime.
* Sponsored by Defense Advanced Research Projects
Agency, Microsystems Technology Office (MTO),
Program: Ultrabeam - The Scaling <strong>of</strong> Coherent
Amplification to the Gamma Ray Region, issued by
DARPA/CMO under Contract No. HR0011-10-C-0105.
"The views and conclusions contained in this document
are those <strong>of</strong> the authors and should not be interpreted as
representing the <strong>of</strong>ficial policies, either expressly or
implied, <strong>of</strong> the Defense Advanced Research Projects
Agency or the U.S. Government."
rhodes@uic.edu
# KFKI Research Institute for Particle and Nuclear
Physics, EURATOM Association, P.O. Box 49,1525,
Budapest, Hungary
DISCUSSION
The use <strong>of</strong> coherent x-rays for the attainment <strong>of</strong>
intensities approaching the Schwinger Limit [8] <strong>of</strong> ~ 4.6 x
10 29 W/cm 2 , a condition initially discussed by Sauter [9]
and Heisenberg and Euler [10], is supported by very
powerful scaling relationships. A summary <strong>of</strong> the key
physical parameters is presented in Fig. (1); the
assessment gives the comparison <strong>of</strong> an infrared source
(ħω ≅ 1eV) with a corresponding source delivering (ħω
≅ 4.5 keV) x-rays. The chief outcome is a figure <strong>of</strong> merit
that measures the propensity to generate a high intensity,
and the x-ray illuminator is favored over the infrared
system by a factor that exceeds 10 21 , a result predicated
on a relationship proportional to ω 6 . Furthermore, it is
known that the overall physical situation governing the
attainment <strong>of</strong> the Schwinger condition is generally
assisted by the existence <strong>of</strong> particularly propitious
geometries <strong>of</strong> irradiation [11,12].
An additional advantage <strong>of</strong> an x-ray wavelength is the
very large elevation <strong>of</strong> the intensity characteristic <strong>of</strong> the
relativistic regime that flows from a fundamental scaling
proportional to ω 2 . Basically, the electric field E
corresponding to the relativistic regime is given by the
condition
eE
mc ω
= 1 (1)
which, for Xe(L) radiation with ħω ≅ 4.5 keV, yields an
intensity <strong>of</strong> ~ 10 25 W/cm 2 . This value is regarded both as
(a) sufficiently high to produce observable consequences
from the dynamics <strong>of</strong> the vacuum [13] and (b) free <strong>of</strong> the
cascade limit for intensities up to the Schwinger/
Heisenberg value, in contrast to the infrared case [14].
The ability to produce stable self-channeled propagation
<strong>of</strong> intense pulses <strong>of</strong> radiation in an underdense
plasma is a well established phenomenon at quantum
energies below ~5 eV [15-18]. An immediate consequence
<strong>of</strong> the availability <strong>of</strong> a high power source <strong>of</strong> coherent
x-rays is the possibility <strong>of</strong> extending the generation
<strong>of</strong> these highly confined stable [16] modes <strong>of</strong> deeply
penetrating propagation to x-ray wavelengths in materials
at solid density. If such channels can be pro-duced with
multi-kilovolt x-rays in high-Z solids, the production <strong>of</strong>
power densities on the order <strong>of</strong> ~ 10 30 W/cm 3 are
projected [19,20].