Discoveries in plasmas while teaching simulation
Section snippets
Two-opposing-cold-streams instability (Fig. 1)
Two opposing electron streams, cold or warm (vt<0.7vdrift) are unstable and grow in time, in a fixed ion background, in a periodic system. In a system where two streams pass each other one wavelength in one period of natural oscillation (of one of the streams), there can be exponential growth of an initial small perturbation. This instability is very old, observed in fluid (e.g., fiord flow over the ocean), and with fast and slow electron streams (amplifier by Haeff [1]), or drifting electrons
Two-opposing-warm-streams instability (Fig. 2)
The interaction of two warm streams is shown here. At t=0, the ratio of thermal velocity to drift velocities vt/vo=0.4. The dispersion relation shows that the m=4 mode has the fastest growth rate. Indeed, at t=30, mode 4 dominates, in the vx–x phase space and in the charge density, ρ. By time 63.6, the 4 phase space vortices have merged, leaving two vortices. By time 244.8, all vortices in phase space have become just one vortex, which is very long lived. The f(v,both streams) is shown in the
Warm plasmas; linear Landau damping, nonlinear heating (Figs. 3–5)
Warm plasmas exhibit simple harmonic oscillations at the plasma frequency, ωp, as known from theory and experiments by Langmuir and Tonks in the 1920s. Much later (1946), using linear kinetic theory, L. Landau [3] found the rate that these oscillations damp in time. Both detailed analysis and physical understanding may be found in [2]. Experimental proof came in the 1960s (e.g., by Malmberg and Wharton, [4], and others). Initial wave energy (electrostatic) is absorbed by the plasma, increasing
Warm plasma between two grounded plates at t=1e–7 (Fig. 6)
Elementary 1d3v bounded warm plasma observations, short circuit, undriven. Starting from an initial uniform plasma between shorted planes, we observe: (a) formation of sheaths; followed by (b) plasma frequency potential oscillations at the central density (symmetric mode); (c) series resonance observed in the current, due to resonance between the capacitive (almost vacuum) sheath and the inductive bulk, resonant at ωseries=ωp(center)[(2s/L)]1/2, where s is the average sheath width and L is the
Summary
Teaching live and interactively can be both exciting and challenging, and have unanticipated surprises, similar to the examples just given. An audience of theorists and experimentalists may be unaccustomed to observing what is occurring inside the plasma (as functions of space, velocity, frequency, wave number, more) as displayed with several dozen diagnostics. In order to improve communication in lecturing and teaching, we have found it advisable to show, say, 1 to 4 live diagnostics at a
Acknowledgements
This work is partially supported by Center for Plasma Theory and Computation, Directed Energy Directorate, Air Force Research Laboratory, Kirtland Air Force Base, New Mexico 87117.
References (7)
The electron-wave tube
Proc. I.R.E
(1949)Longitudinal plasma oscillations
J. Nucl. Energy, Part C, Plasma Phys
(1960)On the vibrations of the electronic plasma
J. Phys. (U.S.S.R.)
(1946)
Cited by (2)
Morphology of radio relics-I. What causes the substructure of synchrotron emission?
2021, Monthly Notices of the Royal Astronomical Society