Abstract
The optical properties of a gas of laserpulse exploded clusters are determined by the time evolving polarizabilities of individual clusters. In turn, the polarizability of an individual cluster is determined by the time evolution of individual electrons within the cluster’s electrostatic potential. We calculate the linear cluster polarizability using the Vlasov equation. A quasistatic equilibrium is calculated from a biMaxwellian distribution that models both the hot and cold electrons, using inputs from a particleincell simulation [T. Taguchi et al., Phys. Rev. Lett.92, 205003 (2004)]. We then perturb the system to first order in the field and integrate the response of individual electrons to the selfconsistent field following unperturbed orbits. The dipole spectrum depicts strong absorption at frequencies much smaller than . This enhanced absorption results from a beating of the laser field with electron orbital motion.
The authors would like to thank J. Cooley for fruitful discussions.
This work was supported by the National Science Foundation and the Department of Energy.
I. INTRODUCTION
II. EQUILIBRIUM CONFIGURATION
III. LINEAR PERTURBATION
A. Linear system
B. Trajectories
C. Algorithm
IV. RESULTS
A. Cold cluster limit
B. Sharp ion profile with single temperature electrons
C. Diffuse ions with single temperature electrons
D. Linear cluster polarizability throughout evolution
V. CONCLUSIONS
Key Topics
 Polarizability
 42.0
 Electric fields
 33.0
 Plasma temperature
 23.0
 Particleincell method
 20.0
 Hot carriers
 15.0
Figures
Comparison of electron density extracted from the PIC simulation (dotted line) and the result of our equilibrium calculation with parameters and extracted from the PIC simulation (solid line) on the left axis. The inset shows the same comparison on a vertical logscale. The corresponding electrostatic potential is plotted on the right scale.
Comparison of electron density extracted from the PIC simulation (dotted line) and the result of our equilibrium calculation with parameters and extracted from the PIC simulation (solid line) on the left axis. The inset shows the same comparison on a vertical logscale. The corresponding electrostatic potential is plotted on the right scale.
Three sample electron trajectories. The cluster radius here is .
Three sample electron trajectories. The cluster radius here is .
The two ion charge density profiles extracted from a PIC code for use in our calculation. The sharp ion density profile (solid) has a very steep gradient at the cluster boundary. The diffuse ion density profile (dotted) trails off smoothly as it approaches the calculation boundary.
The two ion charge density profiles extracted from a PIC code for use in our calculation. The sharp ion density profile (solid) has a very steep gradient at the cluster boundary. The diffuse ion density profile (dotted) trails off smoothly as it approaches the calculation boundary.
Comparison of the real (top graphs) and imaginary (bottom graphs) components of the polarizability spectra from our timedomain kinetic calculation (solid line) and frequency domain fluid calculation (dotted line). A small temperature, , was used in the kinetic calculation. (a) A smoothing factor of is used; (b) the smoothing factor is .
Comparison of the real (top graphs) and imaginary (bottom graphs) components of the polarizability spectra from our timedomain kinetic calculation (solid line) and frequency domain fluid calculation (dotted line). A small temperature, , was used in the kinetic calculation. (a) A smoothing factor of is used; (b) the smoothing factor is .
Comparison of the imaginary component of the polarizability spectra from our timedomain kinetic calculation with frozen particles (solid line), and frequency domain fluid calculation (dotted line). In both cases a smoothing factor of is used. The number of electrons used was and the grid spacing was reduced by a factor 5 to eliminate noise associated with fixed particle location.
Comparison of the imaginary component of the polarizability spectra from our timedomain kinetic calculation with frozen particles (solid line), and frequency domain fluid calculation (dotted line). In both cases a smoothing factor of is used. The number of electrons used was and the grid spacing was reduced by a factor 5 to eliminate noise associated with fixed particle location.
Real (a), and imaginary (b) polarizability spectra resulting from the sharp ion profile. Each spectrum has a vertical offset of and corresponds to a different electron temperature as labeled on the right. The arrow demarcates where a coldcluster dielectric resonance would be expected.
Real (a), and imaginary (b) polarizability spectra resulting from the sharp ion profile. Each spectrum has a vertical offset of and corresponds to a different electron temperature as labeled on the right. The arrow demarcates where a coldcluster dielectric resonance would be expected.
Contours of electron radial (left) and angular (right) frequencies in the energyangular momentum plane. represents a contour level of 0.11. The top graphs are at and the bottom graphs at . The equilibrium distribution function is plotted on the left to elucidate where the electrons are concentrated.
Contours of electron radial (left) and angular (right) frequencies in the energyangular momentum plane. represents a contour level of 0.11. The top graphs are at and the bottom graphs at . The equilibrium distribution function is plotted on the left to elucidate where the electrons are concentrated.
Resonant electron bands in the energyangular momentum plane for the sharp ion profile and . (a) Bands determined by the condition , where corresponds to a wavelength of . The width is chosen for illustrative purposes. (b) Bands determined by the condition , where . The speckles are a numerical artifact.
Resonant electron bands in the energyangular momentum plane for the sharp ion profile and . (a) Bands determined by the condition , where corresponds to a wavelength of . The width is chosen for illustrative purposes. (b) Bands determined by the condition , where . The speckles are a numerical artifact.
Real (a), and imaginary (b) polarizability spectra resulting from the diffuse ion profile. Each spectrum has a vertical offset of and corresponds to a different electron temperature as labeled on the right. The arrow demarcates where a coldcluster dielectric resonance would be expected.
Real (a), and imaginary (b) polarizability spectra resulting from the diffuse ion profile. Each spectrum has a vertical offset of and corresponds to a different electron temperature as labeled on the right. The arrow demarcates where a coldcluster dielectric resonance would be expected.
Resonant electron bands in the energyangular momentum plane for the diffuse ion profile with . (a) Bands determined by the condition , where corresponds to a wavelength of . The width is chosen for illustrative purposes. (b) Bands determined by the condition , where . The speckles are a numerical artifact.
Resonant electron bands in the energyangular momentum plane for the diffuse ion profile with . (a) Bands determined by the condition , where corresponds to a wavelength of . The width is chosen for illustrative purposes. (b) Bands determined by the condition , where . The speckles are a numerical artifact.
Comparison of the imaginary component of the polarizability resulting from the sharp (dotted) and diffuse (solid) ion profile at two different temperatures. The top picture has and the bottom .
Comparison of the imaginary component of the polarizability resulting from the sharp (dotted) and diffuse (solid) ion profile at two different temperatures. The top picture has and the bottom .
(a) On the left axis, the intensity profile (solid) used in irradiating the cluster in the PIC simulation. On the right axis (log scale), hot and cold electron temperatures extracted from the PIC simulation as a function of time (dotted) right axis. (b) On the left axis (log scale), the fraction of hot electrons extracted from the PIC simulation as a function of time (solid). On the right axis, the rms electron radius of the cluster (dotted).
(a) On the left axis, the intensity profile (solid) used in irradiating the cluster in the PIC simulation. On the right axis (log scale), hot and cold electron temperatures extracted from the PIC simulation as a function of time (dotted) right axis. (b) On the left axis (log scale), the fraction of hot electrons extracted from the PIC simulation as a function of time (solid). On the right axis, the rms electron radius of the cluster (dotted).
Real (a), and imaginary (b) polarizability spectra at different times through the cluster evolution as labeled on the right. Each spectrum has a vertical offset of . The spectra were smoothed by a factor . The arrow demarcates where a coldcluster dielectric resonance would be expected.
Real (a), and imaginary (b) polarizability spectra at different times through the cluster evolution as labeled on the right. Each spectrum has a vertical offset of . The spectra were smoothed by a factor . The arrow demarcates where a coldcluster dielectric resonance would be expected.
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