Sourav Pramanik

The transverse magnetic field effect on steady-state solutions of the Bursian diode

A study of steady-states of a planar vacuum diode driven by a cold electron beam (the Bursian diode) under an external transverse magnetic field is presented. The regime of no electrons turned around by a magnetic field only is under the consideration. The emitter electric field is evaluated as a characteristic function for the existence of solutions depending on the diode length, the applied voltage, and the magnetic field strength. At certain conditions, it is shown that a region of non-unique solutions exists in the Bursian diode when the magnetic field is absent. An expression for the maximum current transmitted through the diode is derived. The external magnetic field is put forth to control fast electronic switches based on the Bursian diode.

Phase-mixing of ion plasma modes in pair-ion plasmas

Nonlinear interaction between two electrostatic normal modes of a warm pair-ion plasma, viz., ion plasma mode (Langmuir mode) and ion acoustic mode has been analyzed by employing a perturbation technique. It is shown that a gradual loss of phase coherence in the excited Langmuir wave dynamics (phase-mixing) occurs in such a plasma, leading to wave-breaking at arbitrarily low wave amplitudes. Nonlinear results provide an approximate expression for the phase-mixing time which is found to increase with the increase of the ratio of acoustic frequency to Langmuir frequency. The results of our investigation are expected to be relevant to the laboratory produced paired fullerene-ion plasmas.

Wave breaking of nonlinear electron oscillations in a warm magnetized plasma

Wave breaking phenomena of nonlinear electron oscillations around a homogeneous background of massive ions have been studied in a warm magnetized plasma by using Lagrangian variables. An inhomogeneity in the background magnetic field is shown to induce phase mixing and thus breaking of the oscillations. A nonlinear analysis in Lagrangian variables predicts that wave breaking may disappear above a critical value of the electron temperature. An estimate for the critical temperature has been provided.

A study on the steady-state solutions of a Bursian diode in the presence of transverse magnetic field, when the electrons of the injected beam are turned back partially or totally

The properties of a steady-state planar vacuum diode driven by a cold electron beam have been investigated in the presence of an external transverse magnetic field, employing both the Eulerian and the Lagrangian formalism. With the help of a numerical scheme, the features of the steady-state solutions have been explored in the Eulerian frame, particularly for the case that corresponds to the potential distributions with a virtual cathode. However, exact analytical formulae for the potential and velocity profiles within the inter-electrode region have been derived with the Lagrangian description. In contrast to the previous work [Phys. Plasmas 22, 042110 (2015)], here we have emphasized the situation when electrons are reflected back to the emitter by the magnetic field. Both partial and complete reflection of the electrons due to the magnetic field have been taken into account. Using the emitter electric field as a characteristic parameter, steady-state solutions have been evaluated for specific values of...

Non-neutral plasma diode in the presence of a transverse magnetic field

An analytical study of the plasma states in non-neutral plasma diodes in the presence of an external transverse magnetic field is presented for an arbitrary neutralization parameter γ. Considerations are restricted to the regime where no electrons are turned around by the magnetic field. The emitter electric field strength E0 is used as a characteristic function to investigate the existence of solutions depending on the diode length, the applied voltage, the neutralization parameter, and the magnetic field strength. The potential distribution has a wave form for small magnitudes of the external magnetic field, as well as for the case when magnetic field is absent. A new family of solutions appears along with the Bursian ones. On the other hand, as the Larmor radius becomes comparable with the beam Debye length, oscillations in the potential disappear, and only the Bursian branches remain. Unlike the vacuum diode, there are steady state solutions for the negative values of the emitter field strength. As th...

Effects of magnetic field on phase-mixing of electrostatic oscillations in cold electron-positron-ion plasmas

Spatiotemporal evolution of nonlinear electron-positron oscillations around a homogeneous background of massive ions has been analyzed in cold electron-positron-ion (EPI) plasmas by employing a simple perturbation method, demonstrating phase-mixing and thus wave-breaking of excited oscillations at arbitrarily low amplitudes [C. Maity, Phys. Plasmas 21, 072317 (2014)]. In this work, we investigate effects of the magnetic field on the phase-mixing phenomena of electron-positron oscillations in cold EPI plasmas. A perturbative analysis of governing fluid-Maxwells equations has been carried out up to third order to obtain a rough estimate of the phase-mixing time. It has been shown that the presence of an external ambient magnetic field may induce a delay in the process of phase-mixing of such oscillations.

The phase mixing of an upper hybrid wave in a magnetized pair-ion plasma

The space–time evolution of the electrostatic normal modes (namely, the cyclotron and upper hybrid modes) of a warm pair-ion plasma is studied in the presence of a constant magnetic field. By introducing a phase lag between the density perturbations of positive and negative ions, the nonlinear interaction between these two electrostatic modes is shown. A nonlinear analysis of the basic fluid Maxwell equations based on a perturbative approach shows that excited upper hybrid waves can phase mix away and consequently break at arbitrarily low amplitudes. The phase mixing time is found to increase as the strength of the external magnetic field is enhanced. The results of our investigation are believed to be applicable to laboratory-produced electron–positron and paired fullerene-ion plasmas.

Stability properties of the steady state solutions of a non-neutral plasma diode when there is a uniform magnetic field along transverse direction

The stability properties of a non-neutral plasma diode [Pramanik et al., Phys. Plasmas 23, 103105 (2016)] have been investigated for the stationary states taking arbitrary value of the neutralization parameter. A constant magnetic field is also assumed to be applied externally along the transverse direction. The (η, e)-diagram technique is used to study the stability features of all types of solutions with respect to small aperiodic perturbations. Employing the first order perturbation theory, a relevant dispersion relation has been derived and analyzed for the regimes when electrons are not turned around by the magnetic field. These regimes of solutions belong to the “Normal C branch” and “C-overlap branch” of the “emitter field strength vs. diode gap”-diagrams. With the help of this dispersion relation, both aperiodic and oscillatory stability properties of such solutions have been presented.

Time-independent states of a non-neutral plasma diode when emitted electrons are partially turned around by a transverse magnetic field

An analytical study is presented on the steady states of a plasma diode that is uniformly occupied by infinitely massive ions of constant density and driven by a cold electron beam in the presence of an external transverse magnetic field. In contrast to our previous work [Pramanik et al., Phys. Plasmas 23, 062118 (2016)], here, we investigate the case when electrons are reflected back to the emitter by the magnetic field for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions have been evaluated for the specific values of the diode gap, applied voltage, neutralization parameter, and magnetic field strength. It was found that unlike vacuum diodes (e.g., the Bursian diode), steady state solutions also exist for negative values of the emitter field strength. In case of the Bursian diode, only a single type of solutions (Bursian branches) was observed. However, for the Pierce diode, the new family of solutions appeared al...

A study on the steady-state solutions of a relativistic Bursian diode in the presence of a transverse magnetic field

A comprehensive study on the steady states of a planar vacuum diode driven by a cold relativistic electron beam in the presence of an external transverse magnetic field is presented. The regimes, where no electrons are turned around by the external magnetic field and where they are reflected back to the emitter by the magnetic field, are both considered in a generalized way. The problem is solved by two methods: with the Euler and the Lagrange formulation. Taking non-relativistic limit, the solutions are compared with the similar ones which were obtained for the Bursian diode with a non-relativistic electron beam in previous work [Pramanik et al., Phys. Plasmas 22, 112108 (2015)]. It is shown that, at a moderate value of the relativistic factor of the injected beam, the region of the ambiguous solutions located to the right of the SCL bifurcation point (space charge limit) in the non-relativistic regime disappears. In addition, the dependencies of the characteristic bifurcation points and the transmitted current on the Larmor frequency as well as on the relativistic factor are explored.