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Analysis of the Brunel model and resulting hot electron spectra
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Image of FIG. 1.
FIG. 1.

Configuration of Brunel’s absorption model. A p-polarized plane laser wave (intensity ) impinges under angle and is partially reflected as under . At time instant , the resulting x component penetrates up to the position given by Eq. (1). At the instant τ, its magnitude there is for and zero for .

Image of FIG. 2.
FIG. 2.

Single layer displacement . The individual layer starts from position at the time , indicated in degrees on the ordinate at the right . Only displacements are physically real (a). In the region x>0, the electric field is zero at all times (b).

Image of FIG. 3.
FIG. 3.

Number of particles per unit area returned to the target in the interval .

Image of FIG. 4.
FIG. 4.

Reentry velocity component normal to the target of a layer started at .

Image of FIG. 5.
FIG. 5.

Normalized average reentry energy as a function of reentry time . Bold curve: average over all particles pulled into vacuum during one laser cycle; and dashed curve: average over from Fig. 3.

Image of FIG. 6.
FIG. 6.

Electron spectra f(E) and .

Image of FIG. 7.
FIG. 7.

Absorption coefficient as a function of angle of incidence for under condition ; electron oscillation amplitude in vacuum normalized to light speed c.

Image of FIG. 8.
FIG. 8.

Extended Brunel model, corresponds to Fig. 4 with motion parallel to the target surface included. Dashed: genuine Brunel model, .

Image of FIG. 9.
FIG. 9.

Normalized average reentry energy from the extended Brunel model, corresponds to that from the Brunel model in Fig. 5.

Image of FIG. 10.
FIG. 10.

Electron spectra f(E) and from the extended Brunel model under the condition (solid line). Dashed line from Fig. 5 for comparison.

Image of FIG. 11.
FIG. 11.

Absorption coefficient from the extended Brunel model for (solid line) and from Fig. 7 (dashed).

Image of FIG. 12.
FIG. 12.

1D PIC simulation of collisionless absorption of constant intensities a = 0.3, 1.0, 3.0, and 10 under p-polarized incidence. (a) Spectral energy distribution f(E) of the electrons; vertical line marks the position of E equalizing the mean electron oscillation energy. (b) F(E) total number of electrons having energies greater than and less or equal E; . The number of fast electrons amounts to a few percentage.

Image of FIG. 13.
FIG. 13.

Electron energy spectrum f(E) from Hamiltonian dynamics of a layered target under the action of the Lorentz force from a p-polarized laser beam of intensity Wcm–2 Nd under incidence. The local fields are calculated from Fresnel’s formulas. Anharmonic resonance allows for mixing of layers. Energy cutoff occurs at and .


Generic image for table
Table I.

Comparison of the absorption coefficients as functions of the incident angle from two experiments () and from Brunel’s model (). The meaning of , and is given in the text. and obey the condition .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analysis of the Brunel model and resulting hot electron spectra