97 research outputs found
Above-threshold ionization with highly-charged ions in super-strong laser fields: II. Relativistic Coulomb-corrected strong field approximation
We develop a relativistic Coulomb-corrected strong field approximation (SFA)
for the investigation of spin effects at above-threshold ionization in
relativistically strong laser fields with highly charged hydrogen-like ions.
The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave
function describing the ionized electron laser-driven continuum dynamics
disturbed by the Coulomb field of the ionic core. The SFA in different
partitions of the total Hamiltonian is considered. The formalism is applied for
direct ionization of a hydrogen-like system in a strong linearly polarized
laser field. The differential and total ionization rates are calculated
analytically. The relativistic analogue of the Perelomov-Popov-Terent'ev
ionization rate is retrieved within the SFA technique. The physical relevance
of the SFA in different partitions is discussed.Comment: 11 pages, 4 figure
The Wigner time delay for laser induced tunnel-ionization via the electron propagator
Recent attoclock experiments using the attsecond angular streaking technique
enabled the measurement of the tunneling time delay during laser induced strong
field ionization. Theoretically the tunneling time delay is commonly modelled
by the Wigner time delay concept which is derived from the derivative of the
electron wave function phase with respect to energy. Here, we present an
alternative method for the calculation of the Wigner time delay by using the
fixed energy propagator. The developed formalism is applied to the
nonrelativistic as well as to the relativistic regime of the tunnel-ionization
process from a zero-range potential, where in the latter regime the propagator
can be given by means of the proper-time method.Comment: 5 pages, 4 figure
Above-threshold ionization with highly-charged ions in super-strong laser fields: I. Coulomb-corrected strong field approximation
Aiming at the investigation of above-threshold ionization in super-strong
laser fields with highly charged ions, we develop a Coulomb-corrected strong
field approximation (SFA). The influence of the Coulomb potential of the atomic
core on the ionized electron dynamics in the continuum is taken into account
via the eikonal approximation, treating the Coulomb potential perturbatively in
the phase of the quasi-classical wave function of the continuum electron. In
this paper the formalism of the Coulomb-corrected SFA for the nonrelativistic
regime is discussed employing velocity and length gauge. Direct ionization of a
hydrogen-like system in a strong linearly polarized laser field is considered.
The relation of the results in the different gauges to the
Perelomov-Popov-Terent'ev imaginary-time method is discussed.Comment: 8 pages, 3 figure
Coherent hard x-rays from attosecond pulse train-assisted harmonic generation
High-order harmonic generation from atomic systems is considered in the
crossed fields of a relativistically strong infrared laser and a weak
attosecond-pulse train of soft x-rays. Due to one-photon ionization by the
x-ray pulse, the ionized electron obtains a starting momentum that compensates
the relativistic drift which is induced by the laser magnetic field, and allows
the electron to efficiently emit harmonic radiation upon recombination with the
atomic core in the relativistic regime. In this way, short pulses of coherent
hard x-rays of up to 40 keV energy and 10 as duration can be brought about
Phase-matched coherent hard x-rays from relativistic high-order harmonic generation
High-order harmonic generation (HHG) with relativistically strong laser
pulses is considered employing electron ionization-recollisions from multiply
charged ions in counterpropagating, linearly polarized attosecond pulse trains.
The propagation of the harmonics through the medium and the scaling of HHG into
the multi-kilo-electronvolt regime are investigated. We show that the phase
mismatch caused by the free electron background can be compensated by an
additional phase of the emitted harmonics specific to the considered setup
which depends on the delay time between the pulse trains. This renders feasible
the phase-matched emission of harmonics with photon energies of several tens of
kilo-electronvolt from an underdense plasma
Under-the-barrier dynamics in laser-induced relativistic tunneling
The tunneling dynamics in relativistic strong-field ionization is
investigated with the aim to develop an intuitive picture for the relativistic
tunneling regime. We demonstrate that the tunneling picture applies also in the
relativistic regime by introducing position dependent energy levels. The
quantum dynamics in the classically forbidden region features two time scales,
the typical time that characterizes the probability density's decay of the
ionizing electron under the barrier (Keldysh time) and the time interval which
the electron spends inside the barrier (Eisenbud-Wigner-Smith tunneling time).
In the relativistic regime, an electron momentum shift as well as a spatial
shift along the laser propagation direction arise during the under-the-barrier
motion which are caused by the laser magnetic field induced Lorentz force. The
momentum shift is proportional to the Keldysh time, while the wave-packet's
spatial drift is proportional to the Eisenbud-Wigner-Smith time. The signature
of the momentum shift is shown to be present in the ionization spectrum at the
detector and, therefore, observable experimentally. In contrast, the signature
of the Eisenbud-Wigner-Smith time delay disappears at far distances for pure
quasistatic tunneling dynamics
Estimating the Price Elasticity of Demand for Water with Quasi Experimental Methods
There is a growing recognition in both the professional and popular literatures that water scarcity is a key policy issue that is especially important in arid, urban settings with the prospects for shortfalls in water availability due to the effects of climate change. Those evaluating these types of water problems usually conclude prices must be reformed so that incentives facing water users change to reflect this scarcity. Demand functions provide the basic economic relationships required to understand how water use will respond to such changes. This paper proposes a new method for estimating the price elasticity of demand that meets policy needs and can accommodate the presence of increasing block pricing structures.Water Demand Elasticity, Quasi Experiment, Climate Change, Consumer/Household Economics, Demand and Price Analysis, Environmental Economics and Policy, Resource /Energy Economics and Policy,
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