Numerical investigations of electron-self-injection in different shaped bubbles in wakefield acceleration
الموضوعات : Journal of Theoretical and Applied Physics
Sonu Kumar
1
(Department of Physics, Indian Institute of Technology Delhi, New Delhi, India.)
Dhananjay Singh
2
(Department of Physics, PKRM College, Dhanbad, Jharkhand, India.)
Hitendra K. Malik
3
(Department of Physics, Indian Institute of Technology Delhi, New Delhi, India.)
الکلمات المفتاحية: energy gain, bubble shape, self-injection, Bubble wakefield acceleration,
ملخص المقالة :
Electron-self-injection in bubble wakefield acceleration is the new concept for acceleration of electrons inside bubble. In this technique, self-injected plasma electrons have been used for acceleration whose advantage is that there is no need of external source of electrons. In our case, we have carried out numerical investigations of self-injected plasma electrons in different shaped bubbles such as spherical, longitudinal ellipsoid and transverse ellipsoid bubble. For these numerical investigations, by carrying out relativistic Hamiltonian analysis of plasma electrons, we have used 4th order Runge-Kutta (RK) method by employing MATLAB ode45, a nonstiff differential equations solver. We have discussed different parameters such as impact parameter, radius of bubble, bubble velocity for their effect on the formation of bubbles with different shapes and self-injection of the electrons.
Numerical investigations of electron-self-injection in different shaped bubbles in wakefield acceleration
Sonu Kumar1, Dhanajay. K. Singh2 and Hitendra K. Malik1*
1Plasma Waves and Particle Acceleration Laboratory, Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi - 110016, India
2University Department of Physics, PKRM College, Dhanbad, Jharkhand -826004, India
*Email: hkmalik@physics.iitd.ac.in
Abstract
Electron-self-injection in bubble wakefield acceleration is the new concept for acceleration of electrons inside bubble. In this technique, self-injected plasma electrons have been used for acceleration whose advantage is that there is no need of external source of electrons. In our case, we have carried out numerical investigations of self-injected plasma electrons in different shaped bubbles such as spherical, longitudinal ellipsoid and transverse ellipsoid bubble. For these numerical investigations, by carrying out relativistic Hamiltonian analysis of plasma electrons, we have used 4th order Runge-Kutta (RK) method by employing MATLAB ode45, a nonstiff differential equations solver. We have discussed different parameters such as impact parameter, radius of bubble, bubble velocity for their effect on the formation of bubbles with different shapes and self-injection of the electrons.
Keywords: Bubble wakefield acceleration, plasma, impact parameter, bubble velocity, bubble radius.
1. Introduction
Accelerated charged particles with very high velocity comparable to the light speed, when collide with other moving particles or stationary target, create a huge amount of energy. Today, Large Hadron Collider called as LHC accelerate charged particles in circular track and allow them collide with other charged particles. Sometimes ago, Big-bang concept was tried to be achieved in LHC laboratory for creating the condition of birth of our universe with the help of accelerator concept. Hence, new dimensions of research are possible based on the concept of particle acceleration that has other applications in fusion energy, synchrotron radiation production, nuclear energy, medical treatment and many more. However, such accelerators are huge in size and have very high cost. For example, LHC occupies 27 km of circumference, and its maintenance cost is very high involving a lot of manpower too. The conventional accelerators employ a radiofrequency cavity and have an electrical breakdown problem that limits their efficiency. For removal of such disadvantage, researchers have used the concept of wakefield acceleration, thanks to our pioneer researchers Tajima and Dawson who conceived this acceleration technique. Tajima and Dawson [1] in 1979 created an oscillatory wake in the plasma by introducing electromagnetic field driver called intense short laser pulse; specifically they generated an electron plasma wave corresponding field to which was called wakefield. This wakefield had an advantage of producing three times more accelerator gradient than the one achieved in conventional particle accelerators. Here plasma is used as a medium because it is ionized and is already in breakdown stage. In comparison to size and cost of conventional accelerators, it takes only a few meters in size and has a low cost. For the understanding point of view of the wakefield, the example of a surfer is the best example that uses the wake created by a moving boat in the lake for moving forward. One can visualize the plasma as lake, laser pulse as a driver, and the surfers as charged particles.
In the concept of laser wakefield acceleration (LWFA) [2–4], plasma electrons are expelled by energetic laser photons, creating an electron free region (a region of almost stationary ions). The expelled electrons move back to their positions because of the restoring force due to background ions and overshoot there initial positions because of their inertia and create an electron plasma wave [5]. The frequency of this wave is in the range of electron plasma frequency and accelerator gradient is in GeV/m. There are other methods also for the particle acceleration; for example, the plasma wakefield acceleration (PWFA) where a beam of charged particles drives the wakefield, self-modulated laser wakefield acceleration (SMLWFA) where the laser pulse gets self-modulated and the plasma beat wave wakefield acceleration (PBWA) where two laser beams drive the wakefield [6–9]. Some other wakefield acceleration techniques are their such as proton driven wakefield [10]. In LWFA, a nonlinear plasma wave is generated when the laser’s intensity is quite high, and here a multidimensional wake is created, expelled plasma electrons are trapped around the boundary of the electron free region, i.e. the ion-cavity or the bubble [11–15]. Advantage of this type of wakefield acceleration is that there is no need of externally injected electrons for witness bunch. These electrons are trapped in the first wake at the tail of the bubble and self-injected into the bubble [16–18]. Self-injection of the plasma electrons in bubble wakefield is recent development for the generation of high quality electrons beam [19–28]. These high quality electron beam has been used for many applications such as material characterization [29], generation of synchrotron radiations such as betatron radiations which have been used in medical treatments [30–35] and many more [36–46].
Kostyukov et al. [47] and Lu et al. [14] have developed the model of bubble wakefield and used the spherical shape of the bubble with bubble velocity equal to one. They used a scalar gauge condition and wakefield potential with relativistic Hamiltonian equations analysis, but they did not give the concept of different shapes of bubble during self-injection of the electrons. Trajectory of the plasma electrons has been developed by Lu et al. [48] and bubble structure has been evaluated by Toosi et al. [49]. Li et al. [50] worked for the shape of the bubble by using the electromagnetic field produced inside the bubble and introduced a geometrical parameter such that
defined the spherical bubble and
defined the longitudinal ellipsoid bubble and
defined the transverse ellipsoid bubble. Further work was done by Kumar et al. [17] on different gauges in bubble wakefield acceleration. But no investigation has been done numerically revealing the self-injection process of the plasma electrons and longitudinal and transverse phase-spaces in different shaped bubble regime along with a role of impact parameter, bubble radius and bubble velocity. In the present work, hence, we consider different shapes of the bubble and discuss the phenomenon concerning the electron-self-injection inside the bubbles. We deal with slower as well as faster bubble velocities on the trajectory of the trapped electrons. Our analysis with consideration of the impact parameter defines the radial distance between the trapped electrons and the laser driver.
2. Numerical investigation