asdfuogh wrote:>at high particle count, if you're talking simulating ala particle-to-particle pair interaction, you can use a barnes-hut tree code
http://en.wikipedia.org/wiki/Barnes%E2% ... simulation or a fast multipole method
https://www.siam.org/pdf/news/637.pdf
Depends what physics you are simulating, right? What are the temperatures expected for a Polywell device? Can they be considered collisionless? (I was thinking of tracking particles as in standard PIC codes where you have millions of particles or more.)
Any plasma that produces significant fusion cannot be a collisionless plasma. Perhaps for startup conditions such might be workable , but...
Temperature in a Polywell is a moving target in three ways. So called monoenergetic conditions suggest the ion temperatures, at least, are at a single value. In actuality, the distribution is in a bell curve. You can assume very narrow bell curve distribution to wide distribution similar to the Maxwellian distribution except for some trimming of the high energy tail. Spacial considerations due to the excess electron space charge and radius (position in the potential well for either the ions or electrons) related to the spherical geometry affects speed/ energy and Coulomb cross section and Fusion cross section.. Keep in mind that the shape of the potential well can vary due to ion- electron interactions (ions can drag the light electrons along to a limited degree- a small amount of coupling?) . This does not mean that the collision rate is the same throughout the machine though. Due to the potential well, ideally the ions are fast with long MFP in the core and slow with short MFP on the edge. The opposite for electrons. Despite the increased temperature dependant MFP of ions in the core, the spherical convergence results in exponential increased density in the core.The resultant temperature and density contributions in the core lead to smaller, perhaps much smaller MFP, at least ideally with good convergence. How all this interacts with edge annealing is a complex situation
Modifying considerations: Due to the cusps, upscattered electrons and especially ions (escape electrostatic containment) leave the system faster due to their increased speed (expected number of passes before escape occurs faster). This, I think decreases the high thermal tail distribution of both ions and electrons.
Annealing of ions at the edge may be a major factor in delaying ion thermalization. As the ions stop and turn around at the top of their potential well near the edge of the Wiffleball, the local Coulomb cross section soars and local ion thermalization is ineviitable on one pass. This resets the ion energy distribution that is thermal, but at a low temperature. The distribution is essentially monoenergetic relative to the temperature of the ions deeper in the machine. Certain considerations about MFP in various radii within the machine need to be considered, for annealing to be relavent. There needs to be at least some degree of central confluence/ focus of the ions for edge annealing to be significant.
Note that considering the plasma as a homogenous mixture without central ion confluence is possible for profitable D-D fusion but not for advanced fuels, according to Nebel.
EMC2 recently did computer modeling (for start up conditions?). They used some modified astronomical plasma modeling software.
And finally, here is one presentation of Polywell modeling:
http://iec.neep.wisc.edu/usjapan/16th_U ... shp_14.pdf
Dan Tibbets