Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field
A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field$$\boldsymbol {B}$$inclined at a small angle,$$\alpha \ll 1$$(in radians), to the target. Adiabatic electrons are assumed, requiring$$\alpha \gg \sqrt {Zm_{e}/m_{i}}$$, where$$m_{e}$$and$$m_{i}$$are the electron and ion mass, respectively, and$$Z$$is the charge state of the ion. An electric field$$\boldsymbol {E}$$is present to repel electrons, and so the characteristic size of the electrostatic potential$$\phi$$is set by the electron temperature$$T_{e}$$,$$e\phi \sim T_{e}$$, where$$e$$is the proton charge. An asymptotic scale separation between the Debye length$$\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$$, the ion sound gyro-radius$$\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$$and the size of the collisional region$$d_{c} = \alpha \lambda _{\textrm {mfp}}$$is assumed,$$\lambda _{D} \ll \rho _{s} \ll d_{c}$$. Here$$\epsilon _0$$is the permittivity of free space,$$n_{e}$$is the electron density,$$T_{i}$$is the ion temperature,$$B= |\boldsymbol {B}|$$and$$\lambda _{\textrm {mfp}}$$is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances$$x$$from the wall such that$$\rho _{s} \ll x \ll d_{c}$$, that is, collisions are not treated. A self-consistent solution of the electrostatic potential for$$x \sim \rho _{s}$$is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of$$\phi (x)$$and results in an analytical expression for the ion distribution function at the target. It assumes that$$\tau =T_{i}/(ZT_{e})\gg 1$$, and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For$$\tau \gtrsim 1$, the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.
- Research Organization:
- Univ. of Maryland, College Park, MD (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- FG02-93ER54197
- OSTI ID:
- 1850057
- Journal Information:
- Journal of Plasma Physics, Vol. 87, Issue 1; ISSN 0022-3778
- Publisher:
- Cambridge University Press
- Country of Publication:
- United States
- Language:
- English
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