APDEC-CEMM Collaboration
The Center for Extended MHD Modeling (CEMM) partnered with the Applied Partial Differential Equations Center (APDEC) under the auspices of a Department of Energy SciDAC grant to develop adaptive mesh refinement methods relevant for fusion MHD applications.
Pellet Injection in Tokamaks
Pellet injection is determined to be a reliable method for refueling tokamaks. Experimentally, it is known that the density distribution, after the pellet ablates upon encountering the high temperatures in a tokamak, is not consistent with the distribution inferred from assuming that the ablated material remains on flux surfaces where the ablation occurred. The subsequent redistribution is due to MHD processes. AMR is essential to provide the resolution required to simulate realistic pellet sizes relative to device dimensions (O(0.001)). The image below shows density isosurfaces at a relatively early time during pellet injection. The ablated pellet mass is redistributed at acoustic speed time scales along magnetic field lines (shown in red on the image). Effective uniform mesh resolution for the calculation shown is 512^3
Relevant publications and
presentations.
- R.
Samtaney, S. Jardin, P. Colella, D. Martin. “Simulations of pellet injection using
AMR”, Sherwood Fusion Theory Conference,
Adaptive Mesh Refinement MHD Applications
Adaptive mesh refinement (AMR) provides resolution where required leading to efficient computations. The AMR framework Chombo is used for AMR computations of the following MHD applications. The main effort has been the development of an AMR MHD code for the single fluid resistive MHD equations. The numerical method comprises of an unsplit upwinding formulation (Colella, JCP 1990) of the 8-wave method (Powell et al. JCP 1999). The solenoidal property of the magnetic field is achieved by a projection method which involves the solution of a Poisson equation using a multi-grid technique. The resistive terms are handled in a variety of ways: either explicitly or implicitly. We are also developing a nonlinear resistivity implicit solver.
Magnetic Reconnection
Magnetic reconnection (MR) refers to the breaking and reconnecting of oppositely directed magnetic field lines in a plasma. In the process, magnetic field energy is converted to plasma kinetic and thermal energy. MR occurs in many contexts: for example, in the sawtooth-like oscillations observed in the operation of a tokamak, and in solar coronal events. In general, in MR, two regions are distinguished: an outer “inviscid” region and an inner “resistive” region whose width scales with the inverse square root of the resistivity. We have carried out AMR simulations of the MR process in an idealized two dimensional setting. The objective is to solve the full single-fluid resistive MHD equations and resolve both the outer and the inner regions. AMR provides a significant advantage in resolving the nearly singular current sheets (actually current layers). A time sequence of the y-component of the magnetic field is shown below for a Lundquist number of S=10,000. (Time sequence runs left to right, top to bottom)
The corresponding current images show an unstable current layer which results in the ejection of high pressure plasma. Whether this phenomenon is partially responsible for a reconnection rate faster than that suggested by Sweet-Parker scaling is still an open question.
Relevant publications and
presentations.
- R.
Samtaney, S. Jardin, P. Colella, T. Ligocki. “High-resolution adaptive mesh
simulations of magnetic reconnection”, American Physical Society, DPP
meeting,
- R.
Samtaney and S. Jardin. “An unsplit MHD code with adaptive mesh
refinement”, MHD workshop, General Atomics,
- R.
Samtaney, S. Jardin, P. Colella, T. Ligocki. “Numerical simulations of magnetic
reconnection using AMR”, Sherwood Fusion Theory conference,
Richtmyer-Meshkov Instability
The Richtmyer-Meshkov instability occurs when an interface separating two fluids is subjected to an impulsive acceleration, and is therefore sometime referred to as the “impulsive Rayleigh-Taylor” instability. The original linear stability analysis was done by Richtmyer in 1960 in which he used a shock wave to impulsively accelerate the interface. The experimental confirmation was provided by Meshkov, hence the name Richtmyer-Meshkov (RM). RM and RT are the dominant hydrodynamic instabilities in inertial confinement fusion which inhibit the formation of the “hot spot”, and so these instabilities must be controlled. It was recently discovered that the RM instability is suppressed in the presence of a magnetic field. The images below, taken from AMR simulations of the Ideal MHD equations, illustrate this point.
The top image is the usual RM instability, while the bottom half shows the suppression of the instability and associated mixing at the fluid interface in the presence of a magnetic field.
Relevant publications and
presentations.
- R. Samtaney. “Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field”. Physics fluids, sub judice. Preprint in pdf format.
- R. Samtaney, “The magneto-hydrodynamic Richtmyer-Meshkov instability”. GALCIT Fluid mechanics seminar, Caltech. Also presented as a Computational Plasma Physics seminar, PPPL. Slides in ppt format.
Other
Related talks will go here
when available
Personnel
- Phillip Colella (Head of Applied Numerical Algorithms Group (ANAG), LBNL and PI of APDEC, LBNL)
- Stephen C. Jardin (Co-head of CPPG, PI of CEMM, PPPL)
- Terry J. Ligocki (Member ANAG, LBNL)
- Daniel Martin (Member ANAG, LBNL)
- Peter McCorquodale (Member ANAG, LBNL)
Web page maintained by Shannon Belloni,
PPPL. Last updated: 03/14/05.