3D Two-Fluid Braginskii Simulations of the Large Plasma Device
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Large Plasma Device (LAPD) Model Equations and Numerical Setup Evolution of Turbulence and Transport LAPD Comparisons Conclusions 3D Two-Fluid Braginskii Simulations of the Large Plasma Device Dustin Fishery, Barrett Rogersy, Giovanni Rossi∗, Danny Guice∗ yDepartment of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA ∗Department of Physics and Astronomy , University of California, Los Angeles, California 90095, USA Conclusions: ? 3D global 2-fluid simulations show good agree- ment with data from LAPD in the low-bias pa- rameter regime explored so far. ? KH turbulence at relatively large scales is the dom- inant driver of cross-field transport in the low-bias simulations. ? Biased simulations are currently under study. The work presented here builds upon an initial numerical study [Rogers and Ricci, Phys. Rev. Lett., 104, 2010] of LAPD [Gekelman et al., Rev. Sci. Instrum., 62, 1991] using the Global Braginskii Solver code (GBS) [Ricci et. al., Plasma Phys. Control. Fusion, 54, 2012]. Dustin M. Fisher Sherwood 2015 Modeling the LAPD 1 / 21 Large Plasma Device (LAPD) Model Equations and Numerical Setup Evolution of Turbulence and Transport LAPD Comparisons Conclusions LAPD Primer for a Nominal He Plasma • Plasma 17 m in length, 30 cm in radius • Machine diameter 1m ' • n 2 1012 cm−3 ∼ × • Pulsed at 1 Hz for 10 ms ∼ • Axial magnetic field 1kG ∼ • Te 6 eV and T 0:5 eV ∼ i ∼ • Ion sound gyroradius, ρs 1:4 cm ∼ • Plasma β 10−4 ∼ 012304-2 T. A. Carter and J. E. Maggs Phys. Plasmas 16,012304͑2009͒ Discharge Circuit generation of primary electrons with energy comparable to − + the anode-cathode bias voltage. The mesh anode is 50% Electrical Breaks transparent, allowing half of these primaries to travel down the magnetic field into the main chamber leading to ioniza- tion and heating of the bulk plasma. The cathode is situated B at the mouth of the solenoid and therefore sits in a region of flaring magnetic field. The flared magnetic field maps the 50Ω 73 cm diameter cathode to a ϳ56 cm diameter region in the Cathode Anode main chamber. Primary electrons from the source are isolated 0.2Ω to this region in the chamber and lead to a fast electron Wall Bias Circuit − + tail for rՇ28 cm. Typical plasma parameters in LAPD 12 −3 discharges are ne Շ5ϫ10 cm , Te ϳ7 eV, Ti ϳ1 eV, and BϽ2 kG. In the experiments reported here, the primary T.A. Carter and J.E. Maggs, Physics of Plasmas, 16 (2009) FIG. 1. Schematic of LAPD including wall biasing circuit. plasma species was singly ionized helium and the magnetic http://plasma.physics.ucla.edu/pages/gallery.html (BaPSF) field strength used was 400 G. Modeling18 and spectroscopic measurements show that the ionization fraction of the LAPD Dustin M. Fisher Sherwood 2015 perform a detailedModeling study the of LAPD modifications of turbulence and2 / 21 plasma is տ50% and therefore Coulomb collisions are the turbulent transport in a system free from complications asso- most important collisional process. However, neutral colli- ciated with toroidal systems ͑e.g., field line curvature, poloi- sions ͑charge exchange in particular͒ are important for estab- dal asymmetry, trapped particles͒. Good diagnostic access to lishing the radial current during biasing. LAPD provides for detailed measurements of the spatial and Measurements of density, temperature, floating potential, temporal characteristics of the turbulence. and their fluctuations are made using Langmuir probes. A Here we summarize the primary results reported in this four-tip probe with 0.76 mm diameter tantalum tips arranged paper. Measured turbulent transport flux is reduced and then in a diamond pattern is used as a triple Langmuir probe and suppressed, leading to a confinement transition, as the ap- particle flux probe. Two tips are separated 3 mm along the plied bias is increased. The threshold in the applied bias is field and are used as a double probe to measure ion satura- linked to radial penetration of the driven azimuthal flow. tion current I ϰn ͱT . The remaining two tips are sepa- Two-dimensional measurements of the turbulent correlation ͑ sat e e͒ rated 3 mm perpendicular to the field and measure floating function show that the azimuthal correlation increases dra- potential for deriving azimuthal electric field fluctuations and matically during biasing, with the high-m-number modes in- temperature using the triple Langmuir probe method.24 Ra- volved in turbulent transport becoming spatially coherent. dial particle transport can be evaluated directly using mea- However, no significant change in the radial correlation sured density and electric field fluctuations through Eq. 1 . length is observed associated with the confinement transi- ͑ ͒ Flows are measured using a Gundestrup Mach probe with tion. As the bias is increased above threshold, there is an ͑ ͒ six faces.25 The flow measurements are corrected for the fi- apparent reversal in the particle flux ͑indicating inward trans- nite acceptance angle of the probe faces, which are smaller port͒. The peak amplitude of density and electric field fluc- than the ion gyroradius.26 tuations do decrease, but the reduction is only slight and does Using the difference in floating potential to determine not fully explain the transport flux reduction. The cross- the azimuthal electric field is problematic in the presence of phase between density and electric field fluctuations changes fast electron tails, such as exist on field lines connected to significantly as the threshold for confinement transition is the cathode source. In the presence of fast electrons, differ- reached, and explains the reduction and reversal of the mea- ences in floating potential may no longer be proportional to sured transport flux. The dynamics of the transition have also differences in plasma potential and thus may not accurately been studied and show a correlation between transport sup- measure the electric field. In addition, the fast electron tail, pression and the overlap of the flow ͑shear͒ profile and the which sets floating potential, is much less collisional than the density ͑gradient͒ profile. bulk plasma so that the floating potential is no longer a lo- calized quantity. This delocalization skews the correlation II. EXPERIMENTAL SETUP with locally measured density fluctuations and thereby af- The experiments were performed in the upgraded Large fects the flux measurement. Measurements of Isat are made Plasma Device ͑LAPD͒,21 which is part of the Basic Plasma with a double-Langmuir probe biased to 70 V to reject pri- Science Facility ͑BaPSF͒ at UCLA. The vacuum chamber of mary electrons, and therefore should not be affected by the LAPD is 18 m long and 1 m in diameter and is surrounded fast electron tail. Thus, in this study, we report on the prop- by solenoidal magnetic field coils. The plasma is generated erties of ion saturation fluctuations everywhere in the plasma by a cathode discharge.22 The cathode is 73 cm in diameter column. Properties of electric field fluctuations and cross- and is located at one end of the vacuum chamber, as shown correlation flux measurements are presented everywhere in schematically in Fig. 1. A molybdenum mesh anode is situ- the plasma column, but a caution is issued in regard to mea- ated 50 cm away from the cathode. A bias of 40–60 V is surements made on field lines where primary electrons are applied between the cathode and anode using a solid-state present ͑rՇ28 cm͒. switch,23 resulting in 3–6 kA of discharge current. An im- The edge plasma in LAPD is rotated through biasing the portant aspect of the operation of the plasma source is the vacuum vessel wall positively with respect to the source Downloaded 14 Jun 2010 to 129.170.241.133. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp Large Plasma Device (LAPD) Model Equations and Numerical Setup Evolution of Turbulence and Transport LAPD Comparisons Conclusions Standard Bohm Sheath B.C.'s at the End Walls Vki = ±cs (1) 0 ¨¨* Vke = ±cs exp([Λ − efφplasma − ¨φwallg=Te ]) (2) with p p cs = Te0=mi ; Λ = ln mi = (2πme ) ∼ 3 (3) The B.C.'s on the outflows of ions and electrons to the end walls lead to an approximate global balance Vki ∼ Vke , or φplasma ∼ Λ Te (4) Relaxation due to turbulence Dustin M. Fisher Sherwood 2015 Modeling the LAPD 3 / 21 Large Plasma Device (LAPD) Model Equations and Numerical Setup Evolution of Turbulence and Transport LAPD Comparisons Conclusions The code evolves a set of electrostatic two-fluid drift-reduced Braginskii equations assuming Ti Te : dn @ nV e = − k + Dn (n) + Sn (5) dt @z dTe @Te 2 Te @j = −V e + 0:71 k dt k @z 3 en @z 2 @V e − Te k + Dk (Te ) + DT (Te ) + ST (6) 3 @z Te e 2 dV e @V e 4 η0e @ V e ej me k = −me V e k + k + k dt k @z 3 n @z2 σ k @φ T @n @T + e − e − 1:71 e (7) @z n @z @z 2 dV i @V i 4 η0i @ V i 1 @pe mi k = −mi V i k + k − (8) dt k @z 3 n @z2 n @z 2 d! @! mi Ωci @j = −V i + k − νin! + S! (9) dt k @z e2n @z Dustin M. Fisher Sherwood 2015 Modeling the LAPD 4 / 21 Large Plasma Device (LAPD) Model Equations and Numerical Setup Evolution of Turbulence and Transport LAPD Comparisons Conclusions Evolution of Turbulence and Transport t = 0.25 ms t = 0.40 ms • Starting top-hat 0.5 0.54 shaped density 0.48 source. 0.0 0.42 y (m) • Onset of drift waves 0.36 a) b) 0.5 with kθρs ∼ 0:5, − 0.30 t = 1.13 ms t = 3.33 ms kkLeq ∼ 1.