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(Color online) Two sources of electron radiation in the plasma layer at t = 9.2T 0. (a) Radiation field of the electron sheets [blue (dark gray) line, increased by 90 times for better visibility], radiation of the same sheets calculated for β x = 0 [magenta (medium gray) line, also increased by 90 times], electron density [cyan (light gray) line], vector potential of the standing wave (black line), and electric field of the right-going wave (dashed red line). (b) Phase spaces x − β x [blue (dark gray) line] and x − β y [cyan (light gray) line] for the electrons of the layer. The electrons, which form two radiation sources, are enclosed with ellipses. The parameters of the interaction are the same as in Fig. 1.

(Color online) Two sources of electron radiation in the plasma layer at t = 9.2T 0. (a) Radiation field of the electron sheets [blue (dark gray) line, increased by 90 times for better visibility], radiation of the same sheets calculated for β x = 0 [magenta (medium gray) line, also increased by 90 times], electron density [cyan (light gray) line], vector potential of the standing wave (black line), and electric field of the right-going wave (dashed red line). (b) Phase spaces x − β x [blue (dark gray) line] and x − β y [cyan (light gray) line] for the electrons of the layer. The electrons, which form two radiation sources, are enclosed with ellipses. The parameters of the interaction are the same as in Fig. 1.

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Generation of petawatt-class pulses with a nearly single-cycle duration or with a strongly asymmetric longitudinal profile using a thin plasma layer are investigated via particle-in-cell simulations and the analytical flying mirror model. It is shown that the transmitted pulses having a duration as short as about 4 fs (1.2 laser cycles) or one-cycl...

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... (here and below the momenta are normalized with mc). Note that for an electron, which is free and motionless before interaction with an electromagnetic wave, during interaction, transverse and longitudinal momenta tend to zero simultaneously, and there is no increase for the longitudinal velocity at that times. This effect is clearly seen in Fig. 8(b), where the phase spaces x − β x and x − β y for the electrons are presented. The electrons enclosed with a red ellipse near x ≈ 15.3 have small transverse velocities β y and ultrarelativistic longitudinal velocities β x , which are greater than 0.999 for some of ...
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... opposite directions along x will be considerably greater than the radiation of two motionless sheets. Since for β ⊥ = 0 the radiation field is equal to zero, the peaks of the radiation field will be positioned near these points, where β ⊥ ≈ 0 and β x 1. The radiation field of the electrons at t = 9.2T 0 (just before transmission) is presented in Fig. 8(a) [(blue (dark gray) line, increased by 90 times for better visibility] and in Fig. 5 [green (dark gray) line, increased by 15 times]. The radiation of the electron sheets supposing they are motionless along x is also presented in Fig. 8(a) [magenta (medium gray) line, also increased by 90 times]. These radiations were calculated by ...
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... ≈ 0 and β x 1. The radiation field of the electrons at t = 9.2T 0 (just before transmission) is presented in Fig. 8(a) [(blue (dark gray) line, increased by 90 times for better visibility] and in Fig. 5 [green (dark gray) line, increased by 15 times]. The radiation of the electron sheets supposing they are motionless along x is also presented in Fig. 8(a) [magenta (medium gray) line, also increased by 90 times]. These radiations were calculated by summation of radiation fields of all electron sheets in some cell obtained from Eq. (1) (note that this is the instant radiation and it does not equal the total radiation of the plasma layer at t = 9.2T 0 ). From Fig. 8(a), one can conclude ...
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... along x is also presented in Fig. 8(a) [magenta (medium gray) line, also increased by 90 times]. These radiations were calculated by summation of radiation fields of all electron sheets in some cell obtained from Eq. (1) (note that this is the instant radiation and it does not equal the total radiation of the plasma layer at t = 9.2T 0 ). From Fig. 8(a), one can conclude that, generally, there are two sources producing high-amplitude radiation. One source of radiation is formed in the region, where the electron density is maximal [radiation of the electrons from x 15.7 to x 16 in Fig. 8, also marked with the red ellipse in Fig. 8(b)]. This source is motionless along x (or moves slowly ...
Context 5
... the instant radiation and it does not equal the total radiation of the plasma layer at t = 9.2T 0 ). From Fig. 8(a), one can conclude that, generally, there are two sources producing high-amplitude radiation. One source of radiation is formed in the region, where the electron density is maximal [radiation of the electrons from x 15.7 to x 16 in Fig. 8, also marked with the red ellipse in Fig. 8(b)]. This source is motionless along x (or moves slowly as a whole with the ion velocity) so the role of the longitudinal velocity is not very important here [the radiation field of this source is approximately equal to the radiation of the same sheets calculated for β x = 0; cf. blue (dark ...
Context 6
... the total radiation of the plasma layer at t = 9.2T 0 ). From Fig. 8(a), one can conclude that, generally, there are two sources producing high-amplitude radiation. One source of radiation is formed in the region, where the electron density is maximal [radiation of the electrons from x 15.7 to x 16 in Fig. 8, also marked with the red ellipse in Fig. 8(b)]. This source is motionless along x (or moves slowly as a whole with the ion velocity) so the role of the longitudinal velocity is not very important here [the radiation field of this source is approximately equal to the radiation of the same sheets calculated for β x = 0; cf. blue (dark gray) and magenta (medium gray) lines in Fig. ...
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... in Fig. 8(b)]. This source is motionless along x (or moves slowly as a whole with the ion velocity) so the role of the longitudinal velocity is not very important here [the radiation field of this source is approximately equal to the radiation of the same sheets calculated for β x = 0; cf. blue (dark gray) and magenta (medium gray) lines in Fig. 8(a)]. Because of the very small dimensions of the radiation source (less than λ 0 /2), it can radiate ...
Context 8
... second radiation source is formed by the electron sheets, which are near the point where β y ≈ 0 and β x ≈ 1 (from x 15.2 to x 15.4 in Fig. 8). Here, the role of the longitudinal velocity is very important, and the radiation field of this source is considerably greater than the radiation of the same sheets calculated for β x = 0 [cf. blue (dark gray) and magenta (medium gray) lines in Fig. 8(a) near point x = 15.3]. The maximal amplitude of the radiation of this source can be ...
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... at the position of this electron. So the position of each point where A = 0 and β y = 0 is defined by the vector potential solely and, thus, the radiations of all electrons near this point have the same phase, which is determined by the vector potential [in spite of different longitudinal velocities of the electrons; cf. blue and black lines in Fig. 8(a)]. Before transmission, the points of A = 0 move slowly to the right because the reflected wave has a decreased frequency (due to acceleration of ions and slow motion of the boundary). In this case, the radiation field of such a point cannot sum up coherently and grow in time so the amplitude of the total radiation is small. When ...

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