Exact orbital motion theory of the shielding potential around an emitting, spherical body

Delzanno, G. L.; Bruno, Andrea; Sorasio, G.; Lapenta, Giovanni

doi:10.1063/1.1914546

Cited by 42 publications

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References 42 publications

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“…We note that, for a positively charged grain, the OML formulas do not take into account the fact that a potential well can form near the grain, as shown in Refs. [25,26].…”

Section: A Dust Charging Equationmentioning

confidence: 99%

Survivability of dust in tokamaks: Dust transport in the divertor sheath

Delzanno

Tang

2014

Physics of Plasmas

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The survivability of dust being transported in the magnetized sheath near the divertor plate of a tokamak and its impact on the desired balance of erosion and redeposition for a steady-state reactor are investigated. Two different divertor scenarios are considered. The first is characterized by an energy flux perpendicular to the plate q 0 1 MW/m 2 typical of current short-pulse tokamaks.The second has q 0 10 MW/m 2 and is relevant to long-pulse machines like ITER or DEMO.It is shown that micrometer dust particles can survive rather easily near the plates of a divertor plasma with q 0 1 MW/m 2 because thermal radiation provides adequate cooling for the dust particle. On the other hand, the survivability of micrometer dust particles near the divertor plates is drastically reduced when q 0 10 MW/m 2 . Micrometer dust particles redeposit their material non-locally, leading to a net poloidal mass migration across the divertor. Smaller particles (with radius ∼ 0.1 µm) cannot survive near the divertor and redeposit their material locally. Bigger particle (with radius ∼ 10 µm) can instead survive partially and move outside the divertor strike points, thus causing a net loss of divertor material to dust accumulation inside the chamber and some non-local redeposition. The implications of these results for ITER are discussed.

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“…We note that, for a positively charged grain, the OML formulas do not take into account the fact that a potential well can form near the grain, as shown in Refs. [25,26].…”

Section: A Dust Charging Equationmentioning

confidence: 99%

Survivability of dust in tokamaks: Dust transport in the divertor sheath

Delzanno

Tang

2014

Physics of Plasmas

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“…When electron emission is dominant, the dust grain is positively charged and φ(r) is non-monotonic: the slowest emitted electrons are attracted back to the grain creating a trapped electron population [22,25].…”

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confidence: 99%

“…The emitted electrons experience potential barriers to their motion: depending on v θ , the effective potential can have a maximum or be monotonically decreasing. The position of the maximum r m is given by − One can therefore define a critical tangential velocity, [25], to characterize the electron orbits around the grain. For v θ > v * θ the effective potential is monotonically decreasing (F C ≫ F E ): all the emitted electrons leave the grain, irrespective of their radial velocity.…”

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confidence: 99%

“…The dust grain charges by collecting plasma and emitting electrons. The dynamics of the system is governed by the electric field created by the charged dust and a dynamical equilibrium is reached where the sum of all the currents on the dust surface is zero (floating condition).In order to understand the OML limitations, we recall that the steady state of the system under consideration is completely determined by the orbital motion (OM) theory [23][24][25]. OM is based on the conservation of energy and angular momentum…”

mentioning

confidence: 99%

“…In order to understand the OML limitations, we recall that the steady state of the system under consideration is completely determined by the orbital motion (OM) theory [23][24][25]. OM is based on the conservation of energy and angular momentum…”

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confidence: 99%

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Charging and Heat Collection by a Positively Charged Dust Grain in a Plasma

Delzanno

Tang

2014

Phys. Rev. Lett.

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Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional Orbital-Motion-Limited (OML) theory can break down due to potential well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called OML + approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.PACS numbers: 52.25. Dg, 52.27.Lw, The problem of the charging of a solid body in a plasma has a long history and various applications ranging from probes and spacecraft to planet formation to dusty plasmas in laboratory and space [1]. The body collects plasma particles and is often negatively charged owing to the higher electron mobility. In many instances, however, the body can emit electrons (via thermionic emission, photoemission and secondary electron emission) and become positively charged. [9,10]. Experiments showing the formation of ordered structures with positively charged dust are reported in laboratory [11,12] and in microgravity [13]. Since charging is governed by the characteristic length of the body relative to the plasma Debye length or the electron gyroradius, there is no conceptual difference between the examples above and in what follows we will use the term dust broadly.A charging theory is a necessary ingredient of any model of dust transport and destruction/survival in a plasma [4,6,7,9,[14][15][16][17][18][19]. It calculates the dust charge/potential, momentum and heat collection due to the dust-plasma interaction. The most widely used charging theory is the Orbital-Motion-Limited (OML) theory [20], which leads to a simple nonlinear equation for the dust potential.In this Letter, we use PIC simulations and theoretical analysis to show that OML can become inapplicable in the positively charged regime. It can completely miss the transition between negatively and positively charged dust (thus predicting a positive dust potential when simulations show a negative dust potential) and overestimates the power collected by the grain (up to a factor of 2 for the cases considered). This is due to the development of a non-monotonic potential (a potential well) near the grain. The fact that a potential well can exist near an electron emitting body is known [3,21,22]. However, this is the first study that illustrates the breakdown of OML in this regime. Moreover, this Letter presents a revised charging theory which is as simple as OML, recovers OML in the appropriate limits, but remains accurate when potential well effects are important.We study the charging of a spherical dust grain of radius r d at rest in a collisionless, unmagnetized hydrogen plasma (m e (i) and T e (i) are the electron (ion) mass and temperature, n 0 is the unperturbed plasma density away from the grain). The dust grain charges by collecting plasma and emitting electrons. The dynamics of the system...

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Basic Processes in Complex (Dusty) Plasmas: Charging, Interactions, and Ion Drag Force

Khrapak

Morfill

2009

Contrib. Plasma Phys.

158

131

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Key words Complex (dusty) plasmas, particle charging, interparticle interactions, ion drag force. PACS 52.27.Lw Recent developments in the theoretical investigations of complex (dusty) plasmas -low temperature plasmas containing charged microparticles -are reviewed. The focus is mostly on important basic problems of plasmaparticle interactions, including particle charging, electric potential distribution around the particle, interparticle interactions, and the ion drag force. In particular, the importance of plasma-neutral collisions (especially ionneutral) is emphasized.

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Exact orbital motion theory of the shielding potential around an emitting, spherical body

Cited by 42 publications

References 42 publications

Survivability of dust in tokamaks: Dust transport in the divertor sheath

Survivability of dust in tokamaks: Dust transport in the divertor sheath

Charging and Heat Collection by a Positively Charged Dust Grain in a Plasma

Basic Processes in Complex (Dusty) Plasmas: Charging, Interactions, and Ion Drag Force

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