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Quasi-monoenergetic GeV electrons from the interaction of two laser pulses with a gas

Published online by Cambridge University Press:  12 November 2008

K.P. Singh ,
V. Sajal  and
D.N. Gupta
K.P. Singh*
Affiliation:
Simutech, Gainesville, Florida
V. Sajal
Affiliation:
Department of Physics, Jaypee Institute of Information Technology University, Noida, Uttar Pradesh, India
D.N. Gupta
Affiliation:
Simutech, Gainesville, Florida
*
Address correspondence and reprint requests to: Kunwar Pal Singh, Simutech, 3521 SW 31st. Drive, Gainesville, FL 32608. E-mail: k_psingh@yahoo.com
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Abstract

A scheme is proposed for the acceleration of electrons generated during the ionization of a gas by two laser pulses. The electrons created from the ionization of neutral atoms near the rising edge of the pulse do not gain sufficient energy. If a prepulse is used before the main pulse then the prepulse removes electrons from the outer shells, and the main laser pulse interacts with the electrons in the inner shells of high atomic number gases, such as krypton and argon. The electrons are generated close to the peak of the main laser pulse and gain energy in GeV with a small spread in the energy and low emittance angle.

Keywords

Electron accelerationIonizationLaserPlasmaVacuum
Type
Research Article
Information
Laser and Particle Beams , Volume 26 , Issue 4 , December 2008 , pp. 597 - 604
Copyright
Copyright © Cambridge University Press 2008

INTRODUCTION

The invention of the chirped pulse amplification (CPA) technology (Strickland & Mourou, Reference Strickland and Mourou1985) has led to the focused pulse intensities 1022 W/cm2 (Bahk et al., Reference Bahk, Rousseau, Planchon, Chvykov, Kalintchenko, Maksimchuk, Mourou and Yanovsky2005) and higher. There are efforts to develop a few cycle laser pulses at petawatt (Fuerbach et al., Reference Fuerbach, Fernandez, Apolonski, Fuji and Krausz2005) and exawatt power levels (Carlson et al., Reference Carlson, Nestor, Wasserman and McDowell1970). Such short ultraintense laser pulsed find applications in the acceleration of charged particles (Joshi, Reference Joshi2007).

Quasi-monoenergetic electrons with energies from 100 MeV (Mangles et al., Reference Mangles, Murphy, Najmuddin, Thomas, Collier, Dangor, Divall, Foster, Gallacher, Hooker, Jaroszynski, Lanhley, Mori, Norreys, Tsung, Viskup, Walton and Krushelnick2004; Gedder et al., Reference Gedder, Toth, Tilborg, Esarey, Schroeder, Bruhwiler, Nieter, Cary and Leemans2004; Faure et al., Reference Faure, Glinec, Pukhov, Kiselev, Gordienko, Lefebvre, Rousseau, Burgy and Malka2004; Chen et al., Reference Chen, Unick, Vafaei-Najafabadi, Tsui, Fedosejevs, Naseri, Masson-Laborde and Rozmus2008) to GeV (Leemans et al., Reference Leemans, Nagler, Gonsalves, Toth, Nakamura, Geddes, Esarey, Schroeder and Hooker2006; Glinec et al., Reference Glinec, Faure, Pukhov, Kiselev, Gordienko, Mercier and Malka2005; Koyama et al., Reference Koyama, Adachi, Miura, Kato, Masuda, Watanabe, Ogata and Tanimoto2006; Lifschitz et al., Reference Lifschitz, Faure, Glinec, Malka and Mora2006) and monoenergetic ions (Flippo et al., Reference Flippo, Hegelich, Albright, Yin, Gautier, Letzring, Schollmeier, Schreiber, Schulze and Fernandez2007; Nickles et al., Reference Nickles, Ter-Avetisyan, Schnuerer, Sokollik, Sandner, Schreiber, Hilscher, Jahnke, Andreev and Tikhonchuk2007) have been achieved in laser-plasmas based accelerator. When the laser pulse propagates in plasmas, it excites a longitudinal electric field called the plasma wave, which accelerates the particles to high energies. The simulations have shown that self-injection occurs after the laser intensity increases due to a combination of photon deceleration, group velocity dispersion, and self-focusing. The monoenergetic beam is produced because the injection process is clamped by beam loading and the rotation in phase space that results as the beam dephases (Tsung et al., Reference Tsung, Lu, Tzoufras, Mori, Joshi, Vieira, Silva and Fonseca2006). If the plasma is not fully ionized, the fields of the laser ionize neutral atoms via electron tunneling. The presence of neutral gas density significantly degrades the quality of the Wakefield (Bruhwiler et al., Reference Bruhwiler, Dimitrov, Cary, Esarey, Leemans and Giacone2003). The use of ring laser beams with maximum intensities off-axis as drivers for plasma wave excitation, results in reversal of the focusing and defocusing phase regions in a laser Wakefield accelerator. This improves the performance of self-trapping and laser injection (Michel et al., Reference Michel, Esarey, Schroeder, Shadwick and Leemans2006). The electron bunch can fully ionize the lithium vapor to create plasma. The electrons drive a large amplitude plasma wake that accelerates particles in the back of the bunch by more than 2.7 GeV (Hogan et al., Reference Hogan, Barnes, Clayton, Decker, Deng, Emma, Huang, Iverson, Johnson, Joshi, Katsouleas, Krejcik, Lu, Marsh, Mori, Muggli, O'Connell, Oz, Siemann and Walz2005). The propagation of fast electrons in a gas at different densities has been studied and the role of the density of background material for allowing propagation of fast electrons, the importance of the ionization phase, and the effect of electrostatic fields on fast-electron propagation has been analyzed (Batani et al., Reference Batani, Baton, Manclossi, Santos, Amiranoff, Koenig, Martinolli, Antonicci, Rousseaux, Rabec Le Gloahec, Hall, Malka, Cowan, King, Freeman, Key and Stephens2005). Analytical expressions has been obtained for the Wakefield, density perturbations and the potential behind a laser pulse propagating in a plasma with the pulse duration of the electron plasma period (Malik et al., Reference Malik, Kumar and Nishida2007). Resonant enhancement of electron energy by frequency chirp during laser acceleration in an azimuthal magnetic field in plasma has been studied by Singh and Malik (Reference Singh and Malik2008).

There are very exacting conditions for injecting electrons into short and narrow acceleration buckets in acceleration schemes based on plasma waves. The field strength of the plasma wave is generally smaller than the laser field strength itself. The lasers pulse with focal intensities of 1024 W/cm2, or higher would be available in the near future. The laser fields can accelerate particles to high energies directly. If gas density is sufficiently low to ignore plasma effects, direct acceleration of the electrons by a laser pulse occurs. The electrons are self-injected and accelerated by the laser pulse during the ionization of a gas (Singh, Reference Singh2006). A scheme for electron acceleration by two crossing chirped lasers has been proposed (Gupta & Suk et al., Reference Gupta and Suk2007). The radially polarized laser pulses have been found superior both in the maximum energy gain and in the quality of the produced electron beams (Karmakar & Pukhov, Reference Karmakar and Pukhov2007). The electron injection into high-intensity Gaussian laser pulses via ionization and acceleration of electrons to GeV energies has been studied (Hu & Starace Reference Hu and Starace2002, Reference Hu and Starace2006). The electrons generated close to the rising edge of the laser are trapped by the low intensity and never experience the peak of the pulse and gain low energies.

If we use a prepulse before the main pulse then the electrons are removed from the outer shells of the atoms. The electrons in the inner shells are generated close to the peak of the main laser pulse and efficiently accelerated to multi-GeV energies with a small spread in the energy and low emittance angle. In this paper, we perform three-dimensional (3D) simulations of electron acceleration generated during ionization of a low density gas by two circularly polarized intense laser pulses. This paper is organized as follows: electromagnetic fields and schematic of the electron acceleration process have been described in the next section. The results and discussion are presented in Result and Discussion section. In the final section, the conclusions will be presented.

ELECTROMAGNETIC FIELDS AND SCHEMATIC

Figure 1 shows schematic of electron acceleration from the interaction of two laser pulses with a gas. The prepulse propagates along the x-axis and the main laser pulse propagates along the z-axis. The intensity of the prepulse is lower than the main pulse. The initial position of the peak of the prepulse is closer to the gas than that of the main pulse. The electrons are generated during interaction of high intensity laser pulse with gas atoms through multiple ionizations. The prepulse removes the electrons from the outer shells of the atoms. Then the main laser pulse interacts with the electrons in the inner shells of the atoms. The electrons are generated close to the peak of the main laser pulse and accelerated to high energy in the direction of its propagation.

Fig. 1. (Color online) Schematic of interaction of two laser pulses with a gas.

The prepulse is assumed to be circularly polarized with lowest-order Hermite-Gaussian mode propagating along the x-axis with following electric field

(1)
{\bf E}_1 = \hat{x}E_{1x} + \hat{y}E_{1y} + \hat{z}E_{1z}\comma \; \eqno \lpar 1\rpar

where $E_{1z} = {(E_{10} / f_{1})} \exp [-(\lpar t-\lpar x - x_{L}\rpar /c\rpar ^{2} / \tau^{2}) - (r^{2} / r_{10}^{2} \, f_{1}^{2})$+ iφ], $E_{{\rm l}y} = E_{{\rm 1}z} \exp \left[i ({\pi / 2})\right]$, and $E_{{\rm 1}x} = -({i / k}) (({\partial E_{{\rm 1}z} / \partial z}) +$$ ({\partial E_{{\rm 1}y} / \partial y}))$, where $\phi_{1} = \omega t - kx +\tan^{-1} \lpar x/X_{R}\rpar - ({kr^{2} / 2x}$${\lpar 1 + x/X_{R}\rpar })$, f 12 = 1 + (x/X R)2, X R = kr 102/2 is the Rayleigh length, τ is pulse duration, r 2 = z 2 + y 2, r 10 is spot size of the laser, and x L is the initial position of the pulse peak. We define laser intensity parameter of the prepulse by a 10 = eE 10/m 0ωc.

The magnetic field related to the laser pulse is given by Maxwell's equation ∇ × E1 = −∂B1/∂t. The main pulse is assumed to be circularly polarized with lowest-order Hermite-Gaussian mode propagating along the z axis with following electric field:

(2)
{\bf E} = \hat{x}E_x + \hat{y}E_y + \hat{z}E_z\comma \; \eqno \lpar 2\rpar

where $E_{x} = (E_{0} / f) \exp [-(\lpar t - \lpar z - z_{L}\rpar /c\rpar ^{2} / \tau^{2}) - (r^{2} / r_{0}^{2} f^{2}) + i \phi]$, $E_{y} = E_{x} \exp [i(\pi / 2)], E_{z} = -(i / k) ((\partial E_{x} / \partial x)+ (\partial E_{y} / \partial y))$, where $\phi = \omega t - kz + \tan^{-1} \lpar z/Z_{R}\rpar -kr^2/2z(1+z/Z_R)$, f 12 = 1 + (z/Z R)2, Z R = kr 02/2 is the Rayleigh length, τ is pulse duration, r 2 = x 2 + y 2, r 0 is spot size of the laser, and z L is the initial position of the pulse peak. Longitudinal component E z is very small compared to transverse component E x and E y, however, it plays an important role during electron acceleration. The magnetic field related to the laser pulse is given by Maxwell's equation ∇ × E = −∂B/∂t.

The following equations governing electron momentum are obtained from relativistic Newton–Lorentz equation of motion given by d P/dt = −e(E + v × B),

(3)
{dP_x \over dt} = -eE_x+e\lpar v_z B_y - v_y B_z\rpar \comma \; \eqno \lpar 3\rpar
(4)
{dP_y \over dt} = -eE_y + e\lpar v_x B_z - v_z B_x\rpar \comma \; \eqno \lpar 4\rpar
(5)
{dP_z \over dt} = -eE_z + e\lpar v_y B_x - v_x B_y\rpar \comma \; \eqno \lpar 5\rpar

The equation governing electron energy is given by

(6)
m_0 c^2 {d\gamma \over dt} = -e\lpar v_x E_x + v_y E_y + v_z E_z \rpar \comma \; \eqno \lpar 6\rpar

where −e and m 0 are electron charge and rest mass, respectively. Eqs. (3)–(6) has been simplified using P x = γm 0v x, P y = γm 0v y, P z = γm 0v z, γ2 = 1 + (P x2 + P y2 + P z2)/m 02c 2, a 0 = eE 0/m 0ωc, and b x,y,z = eB x,y,z/m 0ω to obtain following equations

(7)
\gamma {dv_x \over dt} = \lpar v_x^2 - 1\rpar a_x - v_y b_z + v_z b_y + v_x \lpar v_y a_y + v_z a_z\rpar \comma \; \eqno \lpar 7\rpar
(8)
\gamma {dv_y \over dt} = \lpar v_y^2 - 1\rpar a_y - v_z b_x + v_x b_z + v_y \lpar v_x a_x + v_z a_z \rpar \comma \; \eqno \lpar 8\rpar
(9)
\gamma {dv_z \over dt} = \lpar v_z^2 - 1\rpar a_z - v_x b_y+v_y b_x+v_z \lpar v_x a_x + v_y a_y\rpar . \eqno \lpar 9\rpar

Eqs. (7)–(9) are coupled ordinary differential equations, which have been solved numerically by A 3D test-particle simulation code to obtain electron trajectory and momentum. The code uses fifth order Runge-Kutta method described by Romeo et al. (Reference Romeo, Finocchio, Carpentieri, Torres, Consolo and Azzerboni2008) with an adaptive time step size control to achieve a fixed accuracy of the solution. The implementation of the modified efficient algorithm for Runge-Kutta method results in nearly three times reduction in computational time over the classical Runge-Kutta method with an adaptive time step size control. The simulations were run on a computer with Intel Core 2 Quad Q6600 Processor with 4 Gigabyte DDR2 memory. The simulation code was fully parallelized using OpenMP. Implementation of parallelized algorithm results in nearly four times reduction in the computational time. We have achieved nearly 12 times reduction in the computational time using modified efficient algorithm for Runge-Kutta method and using OpenMP.

Short pulse, high field ionization at infrared frequencies typically occurs in the quasiclassical regime in which the field distorts the Coulomb binding potential allowing tunneling of electrons from a bound to a free state. One of the accurate tunneling models in this regime is the Ammosov-Delone-Krainov (ADK) tunneling model. At very high fields, tunneling can be approximated by its classical limit where electrons become free from the Coulomb barrier to a free state (Augst et al., Reference Augst, Meyerhofer, Strickland and Chin1991). This model is known as barrier suppression ionization (BSI) and predicts ionization threshold intensities of tightly bound electrons quite well. We have used this model to calculate ionization time of the bound electrons. The ionization time depends upon laser intensity, atomic number of the atom, and ionization potential of the electrons. We have assumed that the electrons are generated with zero initial energy (initial condition for velocity) at ionization time t 0. The initial position of the atoms at ionization time t 0 gives initial condition for the electron position. As the time progresses, the peak of the pulse approaches the atoms and the electrons are produced through multiple ionization. Ionization module has been incorporated in the code to simulate ionization of deep electron levels of high atomic gases.

It has been found experimentally that plasma effects are insignificant at pressures below 1 Torr (Moore et al., Reference Moore, Ting, Jones, Briscoe, Hafizi, Hubbard and Sprangle2001). At this pressure, plasma density is nearly 1023/m3. The plasma frequency is $\omega_{\,pe} = 5.64 \times 10^4 \sqrt{10^{17}} \cong 1.78 \times 10^{13}$ radian/second. The laser frequency is given by ω = 2πc/λ = 1.88 × 1015 radian per second for λ = 1µm, hence, ωpe2/ω2 ≅ 10−4. Plasma effects such as Wakefields, plasma instabilities, modification of the laser envelope, etc. can be neglected for this plasma density. The simulations presented in this work are valid for gas densities where plasma effects can be ignored.

We define θ = tan−1(r/z). as the electron emission angle between the electron ejection direction and the laser propagation direction z axis. Throughout this paper, time, length, and velocity are normalized by 1/ω, 1/k, and c, respectively. The results have been obtained without and with prepulse. The energy spread factor can be defined by full width at half maximum (FWHM)/ (electron energy at the peak of the energy spectrum). A combination of parameters can be chosen depending upon experimental conveniences and requirements.

One needs to use selective injection via ionization into the high intensity center of the multi-cycle laser pulse to achieve high energy gains. If low atomic number gases are used, the atoms are completely ionized by the rising edge of the laser pulse. The electrons are trapped by the low intensity part of the laser pulse and never experience the peak of the pulse and gain low energy. If we use a high atomic number gas, the electrons are generated throughout from the rising edge to the peak of the laser pulse. The electrons generated close to the rising edge of the pulse gain low energy and the electrons generated close to the peak gain high energy. This results in wide spread in the energy gain and emittance angle. The situation changes when a high atomic number gas and a prepulse are used. The electrons from the inner shells are injected close to the peak of the laser pulse and gain high energy. We show that the electron energy spectra have quasi-monoenergetic features with low angle of emittance in the following description.

RESULTS AND DISCUSSION

The pulse duration is taken to be τ = 200 for both prepulse and main pulse. The laser spot size is taken to be 40 times the laser intensity parameter a 10 for the prepulse, and eight times of the laser intensity parameter a 0 for the main pulse. The initial position of pulse peak is taken at z L = −700 unless specified otherwise. The results throughout this paper are at normalized final time t f = 106.

If the laser intensity is above a threshold related to ionization energy of the bound electron, it can ionize the electron from a shell of the atom. Figure 2a shows the threshold laser intensity parameter a 0th as a function of ionization energy of the bound electrons. The threshold laser intensity parameter a 0th increases quadratically with ionization energy of the bound electrons. Figure 2b shows the ionization time t 0 as a function of degree of ionization for a 0 = 10, 30, 120, and 150 for krypton. The position of the atom is taken at the origin.

Fig. 2. (Color online) (a) The threshold laser intensity parameter a 0th as a function of ionization energy; the ionization time t 0 as a function of degree of ionization for different laser intensities for $\mathop \tau \limits_ \cdot = 200$ and for (b) krypton, and (c) argon.

There is significant difference between the ionization energies of 26 (1205.3 eV), and 27 (2928 eV) electrons of the krypton. There is significant difference between corresponding ionization times of the electrons also. We can utilize this difference between the ionization energies to obtain high energy electrons. Twenty six, 28, and 30 electrons are removed from the krypton atom for laser intensity parameter a 0 = 30, 120, and 150, respectively. We can launch a prepulse with a 10 = 30 to remove 26 electrons of krypton atoms. Remaining four electrons can be accelerated to GeV energies by a high intensity main laser pulse with laser intensity parameter between a 0 = 120, and a 0 = 150. Figure 2c shows the ionization time t 0 as a function of degree of ionization for a 0 = 10, 30, 220, and 250 for argon. There is significant difference between the ionization energy of 16 (918.03 eV) and 17 (4120.89 eV) electrons of the argon. We can utilize this difference between the ionization energies to obtain high energy electrons as well. Sixteen, 17, and 30 electrons are removed from the argon atom for laser intensity parameter a 0 = 30, 220, and 250, respectively. We can launch a prepulse with a 10= 30 to remove 16 electrons of the argon atoms. Remaining two electrons can be accelerated to GeV energies by a high intensity main laser pulse with laser intensity parameter between a 0 = 220, and a 0 = 250.

Figures 3a–3c show electron energy K (in GeV) as a function of normalized ionization time t 0 for a 0= 25, 150, and 250, respectively. The electrons are generated at discreet normalized times. We have considered continuous normalized ionization time t 0 to find its effect on energy gain for the results of these figures. The electrons with initial phases φ0 = (2n + 1)π/2, n = 1, 2, 3, … gain higher energy than the electrons with initial phases φ0 = nπ for a linearly polarized laser pulse. The reason can be explained as follows. When the initial phase is $\phi_0 = n \mathop \pi \limits_ \cdot$, the magnitude of the electric field is zero for a linearly polarized laser pulse. The electric field interacting with electron starts increasing with time, which is an accelerating phase for the electron. When the initial phase is φ0 = nπ, the magnitude of electric field is at its peak for a linearly polarized laser pulse. The electric field interacting with the electron starts decreasing with time, which is a decelerating phase for the electron. The magnitude of electric field does not decrease with time for a circularly polarized laser pulse because it has a y-component of electric field as well. It is evident from Eqs. 1 and 2 that the laser intensity is zero for initial phases φ0 = (2n + 1)π/2 for a linearly polarized laser pulse. The electrons are not generated for these initial phases for a linearly polarized laser pulse. The electrons gain higher energy for a circularly polarized laser pulse than that for a linearly polarized laser pulse due to axial symmetry of the former. We have chosen prepulse as well as main laser pulse as circularly polarized. It can be seen that the electrons close to the peak of the pulse gain highest energy. The energy gain decreases sharply as the distance from the peak of the pulse increases. The highest energies gained by the electrons are 0.26, 9.5, and 26 for a 0 = 25, 150, and 250, respectively. The highest energy gain is proportional to the laser intensity and can be approximated by 0.83a 02.

Fig. 3. (Color online) Electron energy K (GeV) as a function of normalized ionization time t 0 for (a) a 0 = 25, (b) a 0 = 150, and (c) a 0 = 250. The solid red line is for circularly polarized laser pulse. The dotted black and dashed blue lines are for a linearly polarized laser pulse with initial phases φ0 = nπ and φ0 = (2n + 1)π/2, respectively.

The gas atoms are taken randomly distributed from x 0 = −r 0/2 to r 0/2, y 0 = −r 0/2 to r 0/2, z 0 = −150 to 150 for the results of Figures 4 to 8. There is no prepulse for the results of Figures 4 and 5. A prepulse has been used for the results of Figures 6 to 8.

Fig. 4. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy versus angle of emittance (in degree) for krypton for a 0 = 120, 130, 140, and 150 without any prepulse.

Fig. 5. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in eV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for argon for a 0 = 220, 230, 240, and 250 without any prepulse.

Fig. 6. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for krypton for a 0 = 20, 30, and 40 with a prepulse of a 10 = 10.

Fig. 7. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for krypton for a 0 = 120, 130, 140, and 150 with a prepulse of a 10 = 30.

Fig. 8. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for argon for a 0 = 220, 230, 240, and 250 with a prepulse of a 10 = 30.

Figures 4a and 4b show the spectrum of electron energy K (in GeV) and angle of emittance (in degree), respectively, for krypton for a 0 = 120, 130, 140, and 150. The peak of the electron energy is at 0.075, 0.0875, 0.11, and 0.118 GeV for a 0 = 120, 130, 140, and 150, respectively. The energy spread is nearly 100%. The angle of emittance varies from two degree to nine degree. Figures 5a and 5b show the spectrum of electron energy K (in GeV) and angle of emittance (in degree), respectively, for argon for a 0 = 220, 230, 240, and 250. The energy spread is nearly 100%. The angle of emittance varies from one degree to 5.5 degree. The electrons are generated throughout the rising part of the pulse. The electrons generated close to the rising edge of the pulse gain low energy and the electrons generated close to the peak of the pulse gain high energy. This results in wide spread in the energy and emittance angle, degrading the electron beam quality.

The initial positions of the peak of the prepulse and the main pulse are taken at x L = −800 and z L = −1600, respectively, for the results of Figure 6. Figures 6a and 6b show the spectrum of electron energy K (in GeV) and angle of emittance (in degree), respectively, for krypton for a 0 = 20, 30, and 40. The normalized intensity parameter of the prepulse is a 10 = 10. The peak of the electron energy spectrum is at nearly 0.0575, 0.06, and 0.025 GeV for a 0 = 20, 30 and 40, respectively. The energy spread is nearly 80%. The electron generated away from the peak of the pulse gain low energy, which results in spread in the energy. The energy spread is lower than that in Figures 4 and 5. Furthermore, peak of the energy spectrum for a 0 = 20 is comparable to the energy spectrum peak for a 0 = 120. This imply that using two pulses of moderate intensity, we can achieve nearly same energy electrons, and better quality beam than using a single high intensity laser pulse. The peak of emittance spectrum shifts toward lower angle with an increase in the laser intensity. The angle of emittance varies from four degree to nine degree.

We show in Figures 7 and 8 that we can obtain GeV electrons with low energy spread and low emittance using a prepulse and an ultra high intensity laser pulse. The initial positions of the peak of the prepulse and main pulse are taken at x L = −1300 and z L = −2200, and the normalized intensity parameter of the prepulse is a 10 = 30. Figures 7a and 7b show the spectrum of electron energy K (in GeV) and angle of emittance (in degree), respectively, for krypton for a 0 = 120, 130, 140, and 150. The peak of the electron energy spectrum is at nearly 5.5, 5.9, 6.0, and 6.1 GeV for a 0 = 120, 130, 140, and 150, respectively. The energy spread is lowest (nearly 32%) for a 0 = 120. The angle of emittance varies from nearly 0.5 degree to 0.9 degree. Figures 8a and 8b show the spectrum of electron energy K (in GeV) and angle of emittance (in degree), respectively, for argon for a 0 = 220, 230, 240, and 250. The peak of the electron energy is at nearly 20 GeV for all the values of laser intensity parameters a 0 = 220, 230, 240, and 250. The energy spread is nearly 18% for a 0 = 220, which is smallest among the considered laser intensities and other results reported in this paper. The angle of emittance varies from 0.25 degree to 0.5 degree, which is smallest of other results reported in this paper.

The distance of the generated electrons increases from the peak of the pulse with an increase in the laser intensity. It can be seen from Figure 3 that electron energy decreases as the position of the generated electrons increases from the peak of the laser pulse. An increase in the laser intensity causes increase in the electron energy limited by the increase in the distance of the generated electrons from the peak of the pulse. The peak of energy spectrum shifts slightly toward higher energy with an increase in the laser intensity. More electrons are generated at higher laser intensities. The gap between lowest ionization energy and highest ionization energy of the electrons and hence their relative distance with respect to the laser pulse increases. This results in higher spread in the energy gain. The angle of emittance decreases with the increase in the electron energy, hence, the peak of emittance spectrum shifts towards lower angle with an increase in the laser intensity.

Considering normalized laser spot sizes r 0 = 8a 0, real laser spot sizes are nearly 38.2λ, 153λ, and 280λ corresponding to a 0 = 30, 120, and 220, respectively, and real pulse duration is nearly 106λ[µm] fs corresponding to normalized pulse duration τ = 200. Laser intensity is related to intensity parameter a 0 and wavelength by the following relation I[W/cm2] = 1.38 × 1018 (a 0/λ[µm])2. Laser intensities are nearly I = 1.24 × 1021 W/cm2, 2 × 1022 W/cm2, and 6.7 × 1022 W/cm2 for λ = 1 µm and nearly I = 1.24 × 1019 W/cm2, 2 × 1020 W/cm2, and 6.7 × 1020 W/cm2 for λ = 10 µm for a 0= 30, 120 and 220, respectively. The laser wavelength λ = 1.054 µm for the hybrid Ti:sapphire-Nd:glass laser system and λ = 10.6  µm for CO2 laser.

CONCLUSIONS

In conclusion, acceleration of electrons generated during the ionization of krypton and argon by a laser pulse has been studied. The prepulse removes electrons from the outer shells. The electrons in the inner shells of high atomic number gases such as krypton and argon are generated close to the peak of the main laser pulse. These electrons experience high laser intensity near the peak of the pulse and gain energy in GeV. The quality of the electron beams is significantly enhanced. The resulting electron beam is collimated and quasi-monoenergetic. The best results are achieved for argon with prepulse laser intensity parameter a 10 = 30 and main laser intensity parameter a 0 = 120.

ACKNOWLEDGEMENT

This work has been supported by Simutech. All the rights to use this work belong to the company.

References

REFERENCES

Augst, S., Meyerhofer, D.D., Strickland, D. & Chin, S.L. (1991). Laser ionization of noble gases by Coulomb-barrier suppresion. J. Opt. Soc. Am. B 8, 858–867.Google Scholar
Bahk, S.W., Rousseau, P., Planchon, T.A., Chvykov, V., Kalintchenko, G., Maksimchuk, A., Mourou, G.A. & Yanovsky, V. (2005). Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2). Appl. Phys. B. 80, 823–832.CrossRefGoogle Scholar
Batani, D., Baton, S.D., Manclossi, M., Santos, J.J., Amiranoff, F., Koenig, M., Martinolli, E., Antonicci, A., Rousseaux, C., Rabec Le Gloahec, M., Hall, T., Malka, V., Cowan, T. E., King, J., Freeman, R.R., Key, M. & Stephens, R. (2005). Ultraintense laser-produced fast-electron propagation in gas jets. Phys. Rev. Lett. 94, 055004.Google Scholar
Bruhwiler, D.L., Dimitrov, D.A., Cary, J.R., Esarey, E., Leemans, W.P. & Giacone, R.E. (2003). Particle-in-cell simulations of tunneling ionization effects in plasma-based accelerators. Phys. Plasmas 10, 2022–2030.CrossRefGoogle Scholar
Carlson, T.A., Nestor, C.W., Wasserman, N. & McDowell, J.D. (1970). Atomic Data 2, 63 ELI – Extreme Light Infrastructure, European Project. http://www.eli-laser.eu.Google Scholar
Chen, Z.L., Unick, C., Vafaei-Najafabadi, N., Tsui, Y.Y., Fedosejevs, R., Naseri, N., Masson-Laborde, P.E. & Rozmus, W. (2008). Quasi-monoenergetic electron beams generated from 7 TW laser pulses in N-2 and He gas targets. Laser Part. Beams 26, 147–155.CrossRefGoogle Scholar
Faure, J., Glinec, Y., Pukhov, A., Kiselev, S., Gordienko, S., Lefebvre, E., Rousseau, J.P., Burgy, F. & Malka, V. (2004). A laser plasma accelerator producing monoenergetic electron beams. Nature 431, 541–544.CrossRefGoogle ScholarPubMed
Flippo, K., Hegelich, B.M., Albright, B.J., Yin, L., Gautier, D.C., Letzring, S., Schollmeier, M., Schreiber, J., Schulze, R. & Fernandez, J.C. (2007). Laser-driven ion accelerators: Spectral control, monoenergetic ions and new acceleration mechanisms. Laser Part. Beams, 25, 3–8.Google Scholar
Fuerbach, A., Fernandez, A., Apolonski, A., Fuji, T. & Krausz, F. (2005). Chirped-pulse oscillators for the generation of high energy femtosecond laser pulses. Laser Part. Beams 23, 113–116.CrossRefGoogle Scholar
Gedder, C.G.R., Toth, C.S., Tilborg, J. Van., Esarey, E., Schroeder, C.B., Bruhwiler, D., Nieter, C., Cary, J. & Leemans, W.P. (2004). High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding. Nature 431, 538–541.Google Scholar
Glinec, Y., Faure, J., Pukhov, A., Kiselev, S., Gordienko, S., Mercier, B. & Malka, V. (2005). Generation of quasimonoenergetic electron beams using ultrashort and ultraintense laser pulses. Laser Part. Beams 23, 161–166.CrossRefGoogle Scholar
Gupta, D.N. & Suk, H. (2007). Electron acceleration to high energy by using two chirped lasers. Laser Part. Beams 25, 31–36.CrossRefGoogle Scholar
Hogan, M.J., Barnes, C.D., Clayton, C.E., Decker, F.J., Deng, S., Emma, P., Huang, C., Iverson, R.H., Johnson, D.K., Joshi, C., Katsouleas, T., Krejcik, P., Lu, W., Marsh, K.A., Mori, W.B., Muggli, P., O'Connell, C.L., Oz, E., Siemann, R.H. & Walz, D. (2005). Multi-GeV energy gain in a plasma-wakefield accelerator. Phys. Rev. Lett. 95, 054802.Google Scholar
Hu, S.X. & Starace, A.F. (2002). GeV electrons from ultraintense laser interaction with highly charged ions. Phys. Rev. Lett. 88, 245003.CrossRefGoogle ScholarPubMed
Hu, S.X. & Starace, A.F. (2006). Laser acceleration of electrons to giga-electron-volt energies using highly charged ions. Phys. Rev. E 73, 066502.CrossRefGoogle ScholarPubMed
Joshi, C. (2007). The development of laser- and beam-driven plasma accelerators as an experimental field. Phys. Plasmas 14, 055501.Google Scholar
Karmakar, A. & Pukhov, A. (2007). Collimated attosecond GeV electron bunches from ionization of high-Z material by radially polarized ultra-relativistic laser pulses. Laser Part. Beams 25, 371–377.Google Scholar
Koyama, K., Adachi, M., Miura, E., Kato, S., Masuda, S., Watanabe, T., Ogata, A. & Tanimoto, M. (2006). Monoenergetic electron beam generation from a laser-plasma accelerator. Laser Part. Beams 24, 95–100.CrossRefGoogle Scholar
Leemans, W.P., Nagler, B., Gonsalves, A.J., Toth, Cs., Nakamura, K., Geddes, C.G.R., Esarey, E., Schroeder, C.B. & Hooker, S.M. (2006). GeV electron beams from a centimetre-scale accelerator. Nature Phys. 2, 696–699.CrossRefGoogle Scholar
Lifschitz, A.F., Faure, J., Glinec, Y., Malka, V. & Mora, P. (2006). Proposed scheme for compact GeV laser plasma accelerator. Laser Part. Beams 24, 255–259.CrossRefGoogle Scholar
Malik, H.K., Kumar, S. & Nishida, Y. (2007). Electron acceleration by laser produced wake field: Pulse shape effect. Opt. Comm. 280, 417–423.CrossRefGoogle Scholar
Mangles, S.P.D., Murphy, C.D., Najmuddin, Z., Thomas, A.G.R., Collier, J.L., Dangor, A.E., Divall, E.J., Foster, P.S., Gallacher, J.G., Hooker, C.J., Jaroszynski, D.A., Lanhley, A.J., Mori, W.B., Norreys, P.A., Tsung, F.S., Viskup, R., Walton, B.R. & Krushelnick, K. (2004). Monoenergetic beams of relativistic electrons from intense laser plasma interactions. Nature 431, 535–538.Google Scholar
Michel, P., Esarey, E., Schroeder, C.B., Shadwick, B.A. & Leemans, W.P. (2006). Efficient electron injection into plasma waves using higher-order laser modes. Phys. Plasmas 13, 113112.CrossRefGoogle Scholar
Moore, C.I., Ting, A., Jones, T., Briscoe, E., Hafizi, B., Hubbard, R.F., & Sprangle, P. (2001). Measurements of energetic electrons from the high-intensity laser ionization of gases. Phys. Plasmas 8, 2481–2487.CrossRefGoogle Scholar
Nickles, P.V., Ter-Avetisyan, S., Schnuerer, M., Sokollik, T., Sandner, W., Schreiber, J., Hilscher, D., Jahnke, U., Andreev, A. & Tikhonchuk, V. (2007). Review of ultrafast ion acceleration experiments in laser plasma at Max Born Institute. Laser Part. Beams 25, 347–63.CrossRefGoogle Scholar
Romeo, A., Finocchio, G., Carpentieri, M., Torres, L., Consolo, G. & Azzerboni, B. (2008). A numerical solution of the magnetization reversal modeling in a permalloy thin film using fifth order Runge–Kutta method with adaptive step size control. Phys. B 403, 464–468.Google Scholar
Singh, K.P. (2006). Self-injection and acceleration of electrons during ionization of gas atoms by a short laser pulse. Phys. Plasmas 13, 043101.Google Scholar
Singh, K.P. & Malik, H.K. (2008). Resonant enhancement of electron energy by frequency chirp during laser acceleration in an azimuthal magnetic field in a plasma. Laser Part. Beams 26, 363–369.Google Scholar
Strickland, D. & Mourou, G. (1985). Compression of amplified chirped optical pulses. Opt. Commun. 56, 219.Google Scholar
Tsung, F.S., Lu, W., Tzoufras, M., Mori, W.B., Joshi, C., Vieira, J.M., Silva, L.O. & Fonseca, R.A. (2006). Simulation of monoenergetic electron generation via laser wakefield accelerators for 5–25 TW lasers. Phys. Plasmas 13, 056708.Google Scholar
Figure 0

Fig. 1. (Color online) Schematic of interaction of two laser pulses with a gas.

Figure 1

Fig. 2. (Color online) (a) The threshold laser intensity parameter a0th as a function of ionization energy; the ionization time t0 as a function of degree of ionization for different laser intensities for $\mathop \tau \limits_ \cdot = 200$ and for (b) krypton, and (c) argon.

Figure 2

Fig. 3. (Color online) Electron energy K (GeV) as a function of normalized ionization time t0 for (a) a0 = 25, (b) a0 = 150, and (c) a0 = 250. The solid red line is for circularly polarized laser pulse. The dotted black and dashed blue lines are for a linearly polarized laser pulse with initial phases φ0 = nπ and φ0 = (2n + 1)π/2, respectively.

Figure 3

Fig. 4. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy versus angle of emittance (in degree) for krypton for a0 = 120, 130, 140, and 150 without any prepulse.

Figure 4

Fig. 5. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in eV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for argon for a0 = 220, 230, 240, and 250 without any prepulse.

Figure 5

Fig. 6. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for krypton for a0 = 20, 30, and 40 with a prepulse of a10 = 10.

Figure 6

Fig. 7. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for krypton for a0 = 120, 130, 140, and 150 with a prepulse of a10 = 30.

Figure 7

Fig. 8. (Color online) (a) The number of electrons per unit energy (relative scale) versus electron energy K (in GeV) and (b) the number of electrons per unit energy (relative scale) versus angle of emittance (in degree) for argon for a0 = 220, 230, 240, and 250 with a prepulse of a10 = 30.