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list of goals including exploring effects of NBI, rapid repeti- tion of discharges ( 10 min), reproducible plasmas with life- times of at least 5 ms (longer than any characteristic decay times), and reproducibly macro-stable plasmas to allow the study of turbulent fluctuations and transport.8 From the first data taken on C-2 in 2008, to the end of the campaign in early 2014, dramatic strides were taken in terms of opera- tional expertise, plasma quality, and lifetime. The culmina- tion was the High Performance FRC regime (HPF) which combined synergies of NBI, electric end-biasing on open field lines, and advanced wall cleaning techniques to achieve reproducible plasma discharges with lifetimes exceeding 5 ms.11
The upgraded experiment, C-2U, which began its cam- paign in March of 2015, made a number of diagnostic and control upgrades to C-2. The most critical of these extended the success of the HPF regime by upgrading the neutral beam system to six new 15 keV beams with a total power of 10 MW, significantly exceeding the 4 MW total beam power available on the original C-2 machine. In June of 2015, C- 2U achieved sustainment of a plasma for over 5 ms, limited only by the neutral beam pulse length.12
Success on the C-2 and C-2U campaigns in achieving macro-stable, sustained plasma has allowed first measure- ments of turbulent fluctuations to be taken.13 In the current physics regime (1 keV ion temperature, 1019 cm 3 density), particle and energy confinement times scale favorably as temperature is increased.11 The existence of an upper tem- perature limit to this favorable scaling remains an open ques- tion, which is now possible to address due to recent substantive advances in macro-stability control.
B. Character of transport in FRCs
Experimental studies of turbulent transport in FRCs have previously been limited by short experimental confine- ment times. Nonetheless, significant investigations of FRC transport characteristics have been carried out. In most ex- perimental schemes, the FRC is isolated from material walls, and the particle recycling rate is low. To date, beam fueling in real experiments has been absent or small compared to the bulk ion population. Radiative losses and work from mag- netic compression are also typically small. Consequently, the particle and energy confinement times are well approximated by the global particle and energy decay times, respectively. It has also been observed, despite modest collisionality, that electron thermal transport is dominated by convection rather than conduction.14 Because energy is primarily conveyed by particle convection, the energy confinement is governed by the particle confinement.
The nature of confinement varies qualitatively in dif- ferent regions of the plasma. On the closed field lines of the FRC core, confinement is determined by cross-field trans- port. In the 1970s, the lower hybrid drift instability (LHDI) was identified as the most linearly unstable electrostatic micro-instability in this region; however, early numerical simulations of LHDI15–17 overpredict experimentally observed density fluctuations. Electromagnetic micro- instabilities may play a larger role in cross-field transport.
Phys. Plasmas 23, 056111 (2016) Because the equilibrium magnetic field approaches zero at
the O-point, even small magnetic perturbations can connect flux surfaces, allowing electron convection. The need to understand the transport contributions of electrons, in detail, motivates inclusion of electron kinetic responses in the physics simulation model.
Outside the core, it is critical to understand transport across the separatrix, which acts as a boundary condition for both the core and open field line scrape-off layer (SOL). Significant plasma rotation can create a complex separatrix structure not captured by single-fluid MHD, where each spe- cies, a, has unique characteristic surfaces, Pa,18
Pa 1⁄4 qaw þ marua;rot: (1)
Minimally, a two-fluid or kinetic model is required to cap- ture this behavior.
Confinement in the SOL is qualitatively very different from the core and separatrix. Particle transport is a balance of radial diffusion and parallel flow on the open field lines. Parallel flow is strongly influenced by end conditions, which may include field constrictions (e.g., magnetic mirrors), plasma sheaths, and end biasing schemes at the divertor wall. Plasma in the SOL region is not cold. Observations indicate that the temperature in the SOL, just outside the sep- aratrix, is comparable to the core, indicating strong coupling between the regions. As a result, the simulation domain in any transport calculation should include core, separatrix, and SOL.
C. Case for high performance computing (HPC)
The challenge of quantitatively predicting confinement scaling in an advanced beam-driven FRC will require mod- ern high performance computing (HPC). To resolve drift- wave scale turbulence in a domain including the coupled FRC core and SOL regions, a predictive simulation must capture length scales from the device size, 1 m diameter and 10 m in length, down to the length scale of the density gradient, which may be as small as 6 10 5 m just outside the separatrix. Even finer grid resolution may be required. Recent measurements of density fluctuations indicate that electron-scale turbulence, with wavelengths significantly shorter than the ion Larmour radius, dominates in the FRC core.13 Relevant timescales for the problem range from mes- oscale MHD modes down to the electron transit time on a field line in the FRC core. The length of the C-2U device di- vided by the sound speed is on the order of 100 ls, while the electron transit time in the core is 0.2 ls. The need to capture many physics features, including large ion orbits, complex separatrix structure, and electron contributions to both energy transport and turbulence mitigation, motivates use of a kinetic model. Characterizing such a wide range of spatial and temporal scales represents a significant computa- tional challenge, which, to date, is only being addressed by HPC. In the following work, we begin efforts to address this challenge by applying a highly scalable, mature particle-in- cell (PIC) code, the Gyrokinetic Toroidal Code (GTC), to the problem of FRC microinstability.
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