The goal of the Edge Simulation Laboratory (ESL) is to build an edge gyrokinetic code based on continuum (as opposed to particle-in-cell) methods. The code will be runnable as a 4-dimensional (axisymmetric) code on transport timescales, or as a full 5-D turbulence code.  Target applications include edge turbulence and transport, H-mode pedestal physics, and ELM physics. The project will build on experience gained from the edge kinetic code TEMPEST that has been in development at LLNL, as well as from the core code GYRO developed at GA.

In the edge region of fusion devices, the ion drift orbit width can be comparable to the pedestal width (or temperature gradient scale length), and electron and ion mean free paths can be comparable to or exceed scale lengths along a field line.  In consequence, quantitatively significant simulation requires kinetic simulation.  Furthermore, the kinetic simulation must be fully nonlinear (as opposed to the “df” approach commonly used for core simulation, where the distribution function is expanded about a Maxwellian), because the lowest-order distribution function under these conditions is not Maxwellian and not known in advance, and because turbulent fluctuation levels can be locally O (1) or larger.

Since the timescales of interest are long compared to the cyclotron period, gyrokinetics (in which the fast motion of gyration about magnetic field lines is appropriately averaged) is still applicable.  However, the orderings used to derive the gyrokinetic equations used in core codes break down in the edge due to the following important edge physics. First, the pedestal buildup and ELM cycles require a large-amplitude time-dependent inhomogeneous electromagnetic field to be self-consistently included in the gyrokinetic model. Secondly, the characteristic turbulence scale lengths and drift-orbit widths become comparable to the equilibrium radial gradient scale lengths.  A set of generalized gyrokinetic equations, valid for the edge, has been derived by Qin (PPPL) under the auspices of the LLNL LDRD project. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. However, it remains to reduce these equations to a form convenient for coding, and also to develop an appropriately ordered gyrokinetic Coulomb collision operator.

We are adapting continuum, rather than particle-in-cell, techniques.  While a PIC code is in some ways simpler to construct, and is familiar to our group from years of experience with core gyrokinetics, we believe that the continuum approach is preferable for edge simulation.  The issues are particle noise, the computational cost of a suitable PIC-based collision operator, and the relative ease of implementing implicit long-timescale methods.  The usual df approach is inappropriate for the edge, as noted above, and hence one of the principal means of reducing noise in PIC simulation is unavailable. Because we intend to use the kinetic code for both turbulence and transport timescales (in, respectively, 5-dimensional and 4-dimensional instances), implicit techniques are essential to enable long timesteps.  In particular, implicit techniques are needed to do any reasonably efficient simulation of turbulence with kinetic electrons, and particularly when performing transport-timescale simulations with nonlinear transport models (or with nonlinear transport conceivably coming from the 5D instance of the kinetic code itself).  Implicit methods are more straightforward when the entire system is fluid-like equations. Also, we note that core continuum gyrokinetic codes, such as GYRO, GS2 and GENE, have been found to be very successful and productive, robustly able to provide a physically comprehensive treatment (including all the key ingredients for core turbulence: kinetic ions and electrons, electromagnetic fluctuations, equilibrium and turbulence-driven ExB flows, and shaped flux surfaces).  Finally, since PIC edge codes are being developed by the Center for Plasma Edge Simulation (C.S. Chang et al.) and by a group at Helsinki University (Heikkenin et al..), our continuum approach is complementary.

We have chosen to develop a new code rather than retrofitting a core continuum gyrokinetic code such as GYRO, because of complexities attached to edge simulation: the sizeable variation of the electrostatic potential F along magnetic field lines, implying significant variation of a particle’s kinetic energy and particle trapping with turning points that cannot be computed a priori (the solution for F is needed), require different strategies for variable choices and discretization; the divertor geometry implies a more complicated spatial connectivity of regions than in the core; and the equations themselves need to be fully nonlinear and generalized as noted above.

The code is being constructed with field-line-following coordinates to reduce the grid requirements (since edge fluctuations are strongly field-line aligned, and because the plasma equilibrium is also characterized by much longer scale lengths along than across magnetic field lines).  A significant challenge arises when the magnetic field evolves significantly during the simulation, as it likely does during an ELM crash. We hope to address this in the future, should funding allow, by implementing a dynamic grid realignment strategy.


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