13,311 research outputs found
Non-positive curvature and the Ptolemy inequality
We provide examples of non-locally compact geodesic Ptolemy metric spaces
which are not uniquely geodesic. On the other hand, we show that locally
compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we
prove that a metric space is CAT(0) if and only if it is Busemann convex and
Ptolemy.Comment: 11 pages, 2 figure
Nonpositive curvature and the Ptolemy inequality
We provide examples of nonlocally, compact, geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally, compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolem
Helium-3 and Helium-4 acceleration by high power laser pulses for hadron therapy
The laser driven acceleration of ions is considered a promising candidate for
an ion source for hadron therapy of oncological diseases. Though proton and
carbon ion sources are conventionally used for therapy, other light ions can
also be utilized. Whereas carbon ions require 400 MeV per nucleon to reach the
same penetration depth as 250 MeV protons, helium ions require only 250 MeV per
nucleon, which is the lowest energy per nucleon among the light ions. This fact
along with the larger biological damage to cancer cells achieved by helium
ions, than that by protons, makes this species an interesting candidate for the
laser driven ion source. Two mechanisms (Magnetic Vortex Acceleration and
hole-boring Radiation Pressure Acceleration) of PW-class laser driven ion
acceleration from liquid and gaseous helium targets are studied with the goal
of producing 250 MeV per nucleon helium ion beams that meet the hadron therapy
requirements. We show that He3 ions, having almost the same penetration depth
as He4 with the same energy per nucleon, require less laser power to be
accelerated to the required energy for the hadron therapy.Comment: 8 pages, 3 figures, 1 tabl
Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
We study chaotic orbits of conservative low--dimensional maps and present
numerical results showing that the probability density functions (pdfs) of the
sum of iterates in the large limit exhibit very interesting
time-evolving statistics. In some cases where the chaotic layers are thin and
the (positive) maximal Lyapunov exponent is small, long--lasting
quasi--stationary states (QSS) are found, whose pdfs appear to converge to
--Gaussians associated with nonextensive statistical mechanics. More
generally, however, as increases, the pdfs describe a sequence of QSS that
pass from a --Gaussian to an exponential shape and ultimately tend to a true
Gaussian, as orbits diffuse to larger chaotic domains and the phase space
dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in
the International Journal of Bifurcation and Chaos, on Jun 21, 201
Enhancing proton acceleration by using composite targets
Efficient laser ion acceleration requires high laser intensities, which can
only be obtained by tightly focusing laser radiation. In the radiation pressure
acceleration regime, where the tightly focused laser driver leads to the
appearance of the fundamental limit for the maximum attainable ion energy, this
limit corresponds to the laser pulse group velocity as well as to another limit
connected with the transverse expansion of the accelerated foil and consequent
onset of the foil transparency. These limits can be relaxed by using composite
targets, consisting of a thin foil followed by a near critical density slab.
Such targets provide guiding of a laser pulse inside a self-generated channel
and background electrons, being snowplowed by the pulse, compensate for the
transverse expansion. The use of composite targets results in a significant
increase in maximum ion energy, compared to a single foil target case.Comment: 16 pages, 9 figure
Radiation Pressure Acceleration: the factors limiting maximum attainable ion energy
Radiation pressure acceleration (RPA) is a highly efficient mechanism of
laser-driven ion acceleration, with with near complete transfer of the laser
energy to the ions in the relativistic regime. However, there is a fundamental
limit on the maximum attainable ion energy, which is determined by the group
velocity of the laser. The tightly focused laser pulses have group velocities
smaller than the vacuum light speed, and, since they offer the high intensity
needed for the RPA regime, it is plausible that group velocity effects would
manifest themselves in the experiments involving tightly focused pulses and
thin foils. However, in this case, finite spot size effects are important, and
another limiting factor, the transverse expansion of the target, may dominate
over the group velocity effect. As the laser pulse diffracts after passing the
focus, the target expands accordingly due to the transverse intensity profile
of the laser. Due to this expansion, the areal density of the target decreases,
making it transparent for radiation and effectively terminating the
acceleration. The off-normal incidence of the laser on the target, due either
to the experimental setup, or to the deformation of the target, will also lead
to establishing a limit on maximum ion energy.Comment: 17 pages, 6 figure
On the design of experiments to study extreme field limits
We propose experiments on the collision of high intensity electromagnetic
pulses with electron bunches and on the collision of multiple electromagnetic
pulses for studying extreme field limits in the nonlinear interaction of
electromagnetic waves. The effects of nonlinear QED will be revealed in these
laser plasma experiments.Comment: 7 pages, 3 figures, 1 table; 15th Advanced Accelerator Concepts
Workshop (AAC 2012), Austin, Texas, 10-15 June, 201
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