Instability and Disappearance of Debye Sheaths Due to Secondary Electron Emission (SEE). 10/5/12 LTP Teleseminar by Mike Campanell, Grad Student, PPPL. Φ (x) (V). plasma interior. wall. wall. wall. Sheath. plasma interior. No Sheath?. x (m).
Instability and Disappearance of Debye Sheaths
Due to Secondary Electron Emission (SEE)
10/5/12 LTP Teleseminar by Mike Campanell, Grad Student, PPPL
Figure: Potential profiles in a plasma slab bounded by floating walls with moderate emission (black plot) and very strong emission (gray plot).
Figure: Animation of the abrupt change of the electrostatic potential function during sheath instability.
 G.D. Hobbs and J.A. Wesson, Plasma Phys. 9, 85 (1967).  L. A. Schwager, Phys. Fluids B 5, 631 (1993).
Background and Motivation:
Fig: Qualitative differences between (a) the classical sheath, (b) SCL sheath and (c) the new inverse sheath.
 C.A. Ordonez and R.E. Peterkin Jr., J. Appl. Physics. 79, 2270 (1996).
Description of the Simulation Model:
We Simulate Two Cases:
Simulation A – Moderate drift energy case
Ez = 200V/cm, Bx,= 100G, Neutral Density nn = 1012 cm-3 ,Plasma Densitynp = 1011 cm-3
Simulation B – High drift energy case
Ez = 250V/cm (larger VDrift),otherwise similar to Sim. A
 D. Sydorenko, Ph.D. thesis, U. of Saskatchewan, 2006.
Fig: Comparison of Sim. A and Sim. B.
(b) Potential profiles Φ(x).
(c) Φ(x) near the left wall.
(d) Charge density profiles in Sim. A.
(e) Charge density profiles in Sim. B
Time evolution of the flux components in Sim. B.
 Y. Raitses et. al., IEEE Trans. on Plasma Sci. 39, 4, (2011).
Appendix: Why does the inverse sheath not appear in familiar SEE theories?
General SEE theories usually assume ions are drawn to the wall. Poisson’s eq. is then solved with charge densities in the sheath written in terms of a potential Φ(x) that is assumed below the plasma potential.
 G.D. Hobbs and J.A. Wesson, Plasma Phys. 9, 85 (1967).
Sheath Instability in Weakly Collisional Plasmas:
Sheath instabilities can (a) trigger abrupt changes in the plasma, (b) drive oscillations and (c) dramatically increase energy loss and cross-field transport. 
Fig: Illustration of the sheath rapidly collapsing over 5ns. Notice the abrupt drop in the sheath amplitude and the change in the near-wall structure of Φ(x)
 M. Campanell, A. Khrabrov and I. Kaganovich, “General Cause of Sheath Instability Identified for Low Collisionality Plasmas in Devices with Secondary Electron Emission,” PRL 108, 235001 (2012).
Why Does Instability Occur?:
Plot of particle energy components parallel to the walls (Wy + Wz) and perpendicular to the walls (Wx).
Mechanism of Instability:
A decrease of the sheath potential Φallows “weakly confined electrons” (WCE’s) to reach the walls. If the SEE coefficient of the WCE’s exceeds unity, the decrease of Φ causes reduction of the electron surface charge, which further lowers Φ, allowing more WCE’s to reach the wall etc… This leads to a runaway collapse of the sheath.
Verification of the Theory
Fig. Temporal evolution of Φ and partial SEE coefficients in a simulation with Ez, = 140V/cm, Bx,= 100G, Neutral Density nn = 1012 cm-3 ,Plasma Densitynp = 1011 cm-3, turbulent heating rate νturb = 5.6 MHz, H = 2.5cm
Consequence of Instability
Ez, = 200V/cm, Bx,= 100G, nn = 1012 cm-3 , np = 1011 cm-3 νturb = 4.2 MHz, H = 2.5cm
WCE Theory Reveals Cause of Past Observed Instabilities:
 D. Sydorenko et al., Phys. Plasmas. 15, 053506, (2008).  D. Sydorenko et al., PRL 103, 14, (2009).
For More Information on Inverse Sheath:
If you would like a more complete discussion of the inverse sheath phenomenon, please see:
M. D. Campanell, A. Khrabrov and I. D. Kaganovich, “Absence of Debye Sheaths Due To Secondary Electron Emission,” PRL 108, 255001 (2012).
For More Information on Instabilities:
For more detail on the instability phenomena, please see our other paper:
M. D. Campanell, A. V. Khrabrov and I.D. Kaganovich, “General Cause of Sheath Instability Identified for Low Collisionality Plasmas in Devices with Secondary Electron Emission,” PRL 108, 235001 (2012).
(there was a typo in the original email announcement of the talk )
This work was supported by the U.S. Department of Energy and the U.S. Air Force Office of Scientific Research. The PIC code used to obtain the results was written by D. Sydorenko, currently at U. of Alberta.