LOI: Institute for Nonlinear-Laser Studies

       Ulrich Gerlach, Yuji Kodama, and Linn Van Woerkom

MOTIVATION: During the turn of the century a hundred years ago a
confluence of technological advances opened the door  to the studies of
radiation interacting with matter. The concomitant theoretical motivation
and support was provided by quantum mechanics. The fruits of this
integration of  experiment, theory, and technology are now part of
everyday life.

During the past decade a confluence of advances in laser science has
opened the door to the study of laser-matter interaction as the new
frontier of the 21st century. The extraordinarily high intensity
(petawatt) and shortness (attoseconds) of the laser pulses have pushed the
 relativistic, and hence nonlinear, nature of laser-matter interactions to
the forefront of science. These processes are characterized by
ultra-relativistic velocities and accelerations of such extreme violence
that relativistic physics and mathematics is not merely optional but
mandatory.

At present there is a considerable amount of highly visible experimental
activity whose purpose is to grasp the properties and the nature of these
extreme laser processes. However, a mathematically solid understanding in
the form of principles, formulations, equations, etc., is sorely lacking.
A joint physics-mathematics institute -- here at OSU -- whose focus is the
science of extreme laser physics, would go a considerable way in having
the experimental and the theoretical/mathematical aspects flourish 
synergistically.


STRATEGY:  Ingredients for a viable joint physics mathematics institute
are already in place. A core interdisciplinary faculty is providing
intellectual leadership in the intersection of laser physics and dynamical
systems theory.

On one hand this faculty is using laser physics as a source of
nontrivial problems in theoretical physics and mathematics.  Some of
these are documented in a number of tutorials at
http://www.math.ohio-state.edu/~gerlach/laser .  
On the other, it is supplying theoretical motivation and support for
experiments of ultra-intense lasers interacting with matter.

The concomitant investigation of laser-driven electron dynamics has been
opening new vistas in our understanding of fundamental relativistic
interaction processes.  It has also been providing a theoretical template,
which is relativistically exact, yet is characterized by conceptual unit
economy and simplicity.  In addition, this investigation will serve as a 
point of departure for the elucidation of those interaction processes in
which an ultra-intense laser interacts with ultra-relativistic magneto
plasmas, the latter being generated when a target is struck by a
petawatt-class laser beam.   

The success in pushing back the theoretical frontier depends on the
cross-disciplinary synergy of two points of view: (1) that of
theoretical physics characterized by violent accelerations of the type
associated with event horizons and accretion disks of black holes, and
(2) that of mathematics characterized by dynamical systems theory and
nonlinear partial differential equations.  In fact, the combination of
these two points of view augments the robust existence of an Institute
for Nonlinear-Laser Science.


IMPLEMENTATION: At present there is a parallel LOI ("Institute for
Hyper-fast Ultra-relativistic Laser Science") being put forward by the
Physics Department. This LOI focusses primarily on the experimental
aspects of laser science, while the present LOI focusses on theory and
mathematics. The aim is to have a laser institute which accommodates
both theoretical/mathematical and experimental activities.

With or without the Strategic Initiative, Physics plans to proceed
with the formation of a laser institute.  Similarly, with or without
the Strategic Initiative, the mathematical-physics collaboration will
continue, with experiments motivating theory and theory giving
guidance to experiments. The only question is how fast and hence how
notable progress will be made in pushing back the frontier of extreme
laser-matter interaction.

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