PASER: Particle Acceleration by Stimulated Emission of Radiation

Levi Schächter

 Department of Electrical Engineering

Technion – Israel Institute of Technology

Haifa 32000,  ISRAEL

The interaction of electromagnetic radiation with free electrons in the presence of an active medium has some appealing outcomes [1-6].  When an electron moves along a vacuum channel in a dielectric material it may cause radiation to be emitted provided that its velocity is greater than the phase velocity of an electromagnetic plane wave in the medium - this is Cerenkov radiation. What a remote observer measures as electromagnetic energy comes at the expense of the particle's kinetic energy, in other words, the particle is decelerated. For a better understanding of the deceleration force, one has to examine the field distribution in the vicinity of the particle. Ignoring for a moment the presence of the dielectric, a point charge generates in its rest frame of reference an electrostatic field which transforms in the laboratory frame into an infinite spectrum of evanescent waves. As these waves hit the discontinuity between the vacuum channel and the dielectric, a so called secondary field is generated. This is the reaction of the medium to the presence of the charged particle. It is the action of this secondary field which decelerates the electron and it was demonstrated that if instead of a passive dielectric medium, an active medium is used, the action of this secondary field may cause the particle to accelerate.

An additional way to examine the proposed acceleration scheme is to consider the microscopic processes. As indicated above, attached to a moving charge there is an infinite spectrum of evanescent waves; these can be viewed as a spectrum of virtual photons continuously emitted and absorbed by the electron.  These photons impinge upon the excited atom which is conceived here as a two level system in its upper state. Since the spectrum of waves attached to this particle includes the resonance frequency of the medium, a photon with the adequate energy may stimulate the atom. As a result, two correlated photons are emitted:  one is virtual as the initial one and the other is a real photon. Since the two are practically identical, the real photon is absorbed by the moving electron causing to the latter's acceleration. The inverse process is also possible: if the virtual photon encounters an atom in the ground state and excites it, the moving electron loses energy - thus it is decelerated. We may expect net acceleration only if the number of atoms in the excited state is larger than

these in the lower state i.e. the population is inverted. From the description above the acceleration force is a result of stimulated radiation therefore, we call this scheme [1]

PASER which stands for Particle Acceleration by Stimulated Emission of Radiation. This scheme may be conceived as the inverse of Frank-Hertz effect; for the regime of Frank-Hertz experiment namely, one electron-atom collision (in average), the phenomenon was demonstrated experimentally by Latyscheff and Leipunsky [7] in 1930 - the accumulative process is yet to be proven experimentally in the framework of the PASER experiment at Brookhaven National Laboratory.

            A bunch of electrons moving in an active medium excites a wake that is amplified by the medium. The intense radiation field generated in this process reduces the population inversion and as a result, the field-medium interaction reaches saturation. It was shown that the accelerating gradient at saturation may reach the 1GV/m level before the medium is ionized. When ionization occurs, higher gradients may develop provided that we excite resonant states of a partially stripped atom [2-3]. In fact, we determined the set of equations which describe the dynamics of electrons in the presence of a wave propagating in an active medium. Simulation results indicate that even when virtually all the energy is drained from the medium, electrons remain trapped by the accelerating wave [6]. While in previous studies simplifying assumptions on the geometry of the micro-bunch as well as the length of the macro-bunch were made, recently [8] we considered the effect of the active medium on a finite length train of micro-bunches including the dimensions of each micro-bunch.

            The PASER experiment to be performed at Brookhaven National Laboratory aims to demonstrate this result experimentally. Specifically, a 70 MeV electron beam is modulated in a wiggler by an intense CO₂ laser pulse. The modulated electron pulse is then injected into a mixture of a CO₂:N₂:He which is excited by a 200nsec long discharge – if mirrors would have been attached then this cell could have form a laser. Schematics of the experiment is illustrated in Figure 1.

Figure 1:  Schematics of the PASER experiment. A 70 MeV electron beam is modulated in a wiggler by a CO₂ laser beam. The bunched beam is injected in a cell containing CO₂ mixture of gases (CO₂:N₂:He).

The cell contains a CO₂ based mixture at 0.2-0.5atm driven by a capacitor (C=10 nF)  charged to a voltage which is typically less than 35kV – corresponding to 6J of energy. The discharge occurs in a volume of ; according to the power duration the typical pulse is 500 nsec long – the voltage, current, power and energy curves are illustrated in Figure 2.

Figure 2:  Typical current, voltage, power and energy pulses during a typical discharge.

The energy density stored in the medium as a function of the initial capacitor's voltage () is illustrated in Figure 3. In the range of interest this quantity is virtually linearly dependent on .

Figure 3:  Energy density as a function of the initial voltage on the discharge capacitors.

References

1.        Schächter L.; PASER: Particle Acceleration by Stimulated Emission of
            Radiation, Phys. Lett. A ., 205, p. 355 (1995).

2.         Schächter L.;    Particle Acceleration in an Active Medium.

            Phys. Rev. E.  53,  p.6427(1996).

3.         Schächter L.; Amplification of a Wake-Field Generated by a Charged Bunch
            in a Resonant Medium. Phys. Rev. Lett.,  83, p. 92 (1999).

4.         Schächter L.; Hybrid Cerenkov Mode in a Resonant Medium.
            Phys. Rev. E, 62, p.1252 (2000).

5.         Schächter L.; Resonant Absorption Instability. Phys. Lett. A, 277, p.65 (2000).

6.         Schächter L.; Colby E.  and Siemann R.H.; Saturation of Bunch-Wave
             Interaction in an Active Medium, Phys. Rev. Lett., 87, 134802 (2001).

7.         Latyscheff and Leipunsky; Z. Phys. 65, p.111 (1930).

            See also  Collisions of the Second Kind by E.J.B. Wiley, Edward Arnold &
            Co., London,  pp. 6-38, (1937). More recently: K.L. Tan and A. von Engel,
            Proc. Roy. Soc. Lon. A. 324, p.183 (1971).

8.         Schächter L.;  Train of Micro-Bunches in an Active Medium

            Advanced Acceleration Concepts 2004, June 21-26, Stony Brook, USA (2004)