PHYSICAL REVIEW E 101, 053206 (2020) Mitigation of multispecies Weibel instability in a finite non-neutral magnetized beam-plasma system Sam Yaghoubi , Abbas Ghasemizad, * and Soheil Khoshbinfar Department of Physics, Faculty of Science, University of Guilan, P.O. Box 41335-1914 Rasht, Iran (Received 5 February 2020; accepted 22 April 2020; published 21 May 2020) Compressing and charge neutralization of the heavy-ion beam in an inertial fusion reactor are considered as pivotal processes for increasing the energy gain. For this purpose, the ion beam is usually transported through the plasma channel so that multispecies Weibel instability can grow in this system. Recently, a small solenoidal magnetic field has been added to this method to have additional control of these processes. On the other hand, charge and current may not be completely neutralized in this transport; as a result, the fractional charge and current neutralization can affect the growth rate of this instability. In this work, the dispersion equation has been obtained in cylindrical, cold, magnetized, non-neutral plasma in the macroscopic fluid frame. Numerical results show that if the electron cyclotron frequency of the background plasma normalized by plasma frequency is larger than the ion beam velocity normalized by the speed of light, as well as the current fraction being smaller than 1/2, the eigenmodes of multispecies Weibel instability can be completely stabilized. Moreover, these results are valid when the percent deviation from the charge-neutral state is positive. In the negative regime of percent deviation, the instability increases drastically so that the system can be completely unstable only for more than 2%. Therefore, selecting the radius of the ion beam smaller than the electron skin depth of the plasma and the beam pulse duration much longer than the plasma oscillation time are proposed for quenching of this instability. DOI: 10.1103/PhysRevE.101.053206 I. INTRODUCTION Neutralization of the ion beam charge and current states by the background plasma is an important issue in broad research areas which involves the transport of fast particles in plasma, especially in astrophysics [1–4], accelerators [4,5], and inertial confinement fusion [6–9]. The successful trans- port and focusing of the relativistic ion beam in the inertial fusion reactor core on the submillimeter-sized target is a challenging task. It is usually difficult to reduce the focal spot of the incident ion such as lithium, potassium, or cesium from several centimeters to a few millimeters [10,11]. The latest proposed technique to tackle this problem has been applied in the Neutralized Drift Compression eXperiment (NDCX) project at the collaborative program of LBNL, LLNL, and PPPL. In this project, an ion beam with an initial particle density of 10 10 − 10 14 cm −3 was injected into a cylindrical waveguide that previously was filled by a cold, collisionless plasma having the temperature 1–10 eV [12,13]. In this process, the density and the temperature of the beam reach 100 times the initial value, while the radius of the beam has decreased from a few centimeters to several millimeters [14]. Recently, the application of a solenoidal magnetic field in a more advanced project, NDCX-II, provides additional control on the focusing of the ion beam. Here the magnetized plasma responses to the injection of the intense ion beam excite the micro-instabilities such as multispecies two-stream and Weibel instabilities [15–18]. Moreover, the Whistler instabil- ity and helicon waves may grow in this medium, provided that ω ce /ω e  2 β b , where ω ce , ω e , and β b are the cyclotron * Corresponding author: ghasemi@guilan.ac.ir frequency, plasma electron frequency, and ion beam velocity to the speed of light, respectively [19]. This research has been focused on the weak magnetic field (ω ce /ω e  2 β b ); consequently, there are no Whistler and heli- con waves in this medium. However, there still exists concern about the linear growth rate of the multispecies two-stream and Weibel instabilities in the non-neutral magnetized plasma. In most cases, the two-stream instability exhibits a much faster growth rate than the Weibel instability; however, it finally reduces the beam quality by pinching [20]. An overview of multispecies Weibel instability in the absence of the external magnetic field may be found in Ref. [15]. There, by using the fluid model, the growth rate of this unstable mode in the finite neutral state was discussed, and for the nonconstructive situation of the system, the optimum lengths of the plasma channel were also derived. Moreover, other studies on the magnetized infinite plasma in the neutral state, especially Ref. [18] on the NDCX project, have confirmed that the axial external magnetic field can moderate the growth rate of the Weibel instability [21,22]. There is some evidence that charge and current states in the beam-plasma system may deviate from the neutral state. The electron response time to the injection of the ion beam is estimated with the electron plasma frequency (T response = 2π/ω pe )[23]. So, if the pulse duration of the incident ion beam is smaller than the response time, the ion beam can experience the charge and current non-neutrality during the compression stage. The application of a small magnetic field of ∼100 G may destabilize the beam neutralization. More- over, it has been pointed out that the axial magnetic field satisfying the condition of ω ce /ω e  β b strongly affects the degrees of charge and current neutralization [24,25]. In a non- magnetized plasma, for a thin beam (Z b n b  n p ), the plasma 2470-0045/2020/101(5)/053206(10) 053206-1 ©2020 American Physical Society