Charged Particle Motion in a Highly Ionized Plasma

A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g=e^2\kappa_D/ 4\pi T is small, where \kappa_D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, dE/dx is of the generic form g^2 \ln[C g^2]. The precise numerical coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker-Planck equation that describes particle motion in the plasma. The coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker-Planck equation describes the longitudinal straggling and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.Comment: Comments: Published in Phys. Rep. 410/4 (2005) 237; RevTeX, 111 Pages, 17 Figures; Transcription error corrected in temperature equilibration rate (3.61) and (12.44) which replaces \gamma-2 by \gamma-

Temperature equilibration in a fully ionized plasma: electron-ion mass ratio effects

Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These precise calculations are accurate to leading and next-to-leading order in the plasma coupling parameter, and to all orders for two-body quantum scattering within the plasma. Classical molecular dynamics can provide another approach that can be rigorously implemented. It is therefore useful to compare the predictions from these two methods, particularly since the former is theoretically based and the latter numerically. An agreement would provide both confidence in our theoretical machinery and in the reliability of the computer simulations. The comparisons can be made cleanly in the purely classical regime, thereby avoiding the arbitrariness associated with constructing effective potentials to mock up quantum effects. We present here the classical limit of the general result for the temperature equilibration rate presented in BPS. We examine the validity of the m_electron/m_ion --> 0 limit used in BPS to obtain a very simple analytic evaluation of the long-distance, collective effects in the background plasma.Comment: 14 pages, 4 figures, small change in titl

Root Growth and Development of Float Tobacco Transplants Before and After Transplanting

In the production of float tobacco transplants, the seedling produces at least two different kinds of roots. The “media” roots are those that grow in the soilless medium within the float tray cell. They have a normal branched appearance similar to roots produced on soil-bed grown transplants. The “water” roots grow through the soilless medium in tray cells and into the nutrient solution below the float tray. They tend to be very fragile and less branched than roots growing in the soilless medium. In removal of seedlings from tray cells during transplanting, “water” roots are usually badly damaged or destroyed, which could affect establishment of transplants in the field since the most critical period in the development of tobacco plants occurs immediately after transplanting. When these young plants are removed from the protective environment of the float bed system and are subjected to radically different and sometimes adverse field conditions, stress on the juvenile plants is created. Field establishment of these young plants is dependent upon growth or new formation of the “media” and “water” roots. To maximize establishment of transplants, it is important to know how the \u27\u27water roots and the media roots develop in the float system and their contribution to transplant establishment during the first few weeks after transplanting. The objectives of this study were: 1) to characterize the growth of media and \u27\u27water roots on tobacco seedlings in the float system, and 2) to assess tobacco transplant growth with or without \u27\u27water\u27\u27 roots, at two and four weeks after transplanting

Charged Particle Motion in a Plasma: Electron-Ion Energy Partition

A charged particle traversing a plasma loses its energy to both plasma electrons and ions. We compute the energy partition, the fractions $E_e/E_0$ and E_\smI/E_0 of the initial energy $E_0$ of this `impurity particle' that are deposited into the electrons and ions when it has slowed down into an equilibrium distribution that we shall determine. We use a well-defined Fokker-Planck equation for the phase space distribution of the charged impurity particles in a weakly to moderately coupled plasma. The Fokker-Planck equation holds to first sub-leading order in the dimensionless plasma coupling constant, which means we compute to order $n\ln n$ (leading) and $n$ (sub-leading) in the plasma density $n$. Previously, the order $n$ terms had been estimated, not calculated. Since the charged particle does not come to rest, the energy loss obtained by an integration of a $dE/dx$ has an ambiguity of order of the plasma temperature. Our Fokker-Planck formulation provides an unambiguous, precise definition of the energy fractions. For equal electron and ion temperatures, we find that our precise results agree well with a fit obtained by Fraley, Linnebur, Mason, and Morse. The case with differing electron and ion temperatures, a case of great importance for nuclear fusion, will be investigated in detail in the present paper. The energy partitions for this general case, partitions that have not been obtained before, will be presented. We find that now the proper solution of the Fokker-Planck equation yields a quasi-static equilibrium distribution to which fast particles relax that has neither the electron nor the ion temperature. This "schizophrenic" final ensemble of slowed particles gives a new mechanism to bring the electron and ion temperatures together. The rate at which this new mechanism brings the electrons and ions in the plasma into thermal equilibrium will be computed.Comment: Improved abstract, introduction, and conclusion

The energy partitioning of non-thermal particles in a plasma: or the Coulomb logarithm revisited

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated to leading and next-to-leading order by Brown, Preston, and Singleton (BPS). After reviewing the main ideas behind this calculation, we use a Fokker-Planck equation derived by BPS to compute the electron-ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion -- more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible, as this could have implications for the Laser Megajoule (LMJ) facility in France and the National Ignition Facility (NIF) in the United States. The traditional method by which one calculates the electron-ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron-ion energy splitting breaks down. As a result, the method suffers a systematic error of order T/E0, where T is the plasma temperature and E0 is the initial energy of the charged particle. In the case of DT fusion, for example, this can lead to uncertainties as high as 10% or so. The formalism presented here is designed to account for the thermalization process, and in contrast, it provides results that are near-exact.Comment: 10 pages, 3 figures, invited talk at the 35th European Physical Society meeting on plasma physic

Effect of Seed Pellet Modification on Spiral Root Formation of Tobacco Seedlings

Tobacco seeds are often pelleted to facilitate precision seeding into float trays. Pelleting consists of the application of solid particles, such as clay, to seeds with a binder in a coating pan or tumbling drum to form spherically shaped dispersal units. One of the several advantages of pelleting is to provide seeds with a vastly enlarged bulk size to ensure proper placement of the seed at the surface of the growing medium

Acoustic Sorting Models for Improved Log Segregation

In this study, we examined three individual log measures (acoustic velocity, log diameter, and log vertical position in a tree) for their ability to predict average modulus of elasticity (MOE) and grade yield of structural lumber obtained from Douglas-fir (Pseudotsuga menziesii [Mirb. Franco]) logs. We found that log acoustic velocity only had a moderate correlation with average MOE of the lumber produced from the logs (R2 = 0.40). Log diameter had a weak correlation with average lumber MOE (R2 = 0.12). Log vertical position in a tree was found to have a relatively good relationship with lumber MOE (R2 = 0.57). Our analysis also indicated that the combinations of log acoustic velocity and log diameter or log acoustic velocity and log position were better predictors of average lumber MOE and lumber visual grade yield than log acoustic velocity alone. For sorting best quality logs, multivariable models were more effective than the velocity-alone model; however, for sorting poorest quality logs, the velocity-alone model was as effective as multivariable models

Quality of Emergency Care on the Night Shift

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72839/1/j.aem.2005.09.005.pd