arXiv subjects

Lowell S. Brown

Publications and source records attributed to Lowell S. Brown.

At least 19 recordsLinked to original sources

arXiv2013

Field Theory of the d+t -> n+alpha Reaction Dominated by a 5He* Unstable Particle

An effective, non-relativistic field theory for low-energy d+t -> n+alpha reaction is presented. The theory assumes that the reaction is dominated by an intermediate 5He* unstable spin 3/2+ resonance. It involves two parameters in the coupling of the d+t and n+alpha particles to the unstable resonant state, and the resonance energy level -- only three real parameters in all. All Coulomb corrections to this process are computed. The resultant field theory is exactly solvable and provides an excellent description of the d+t fusion process.

nucl-th↗

arXiv2013

Effective field theory as a limit of R-matrix theory for light nuclear reactions

We study the zero channel radius limit of Wigner's R-matrix theory for two cases, and show that it corresponds to non-relativistic effective quantum field theory. We begin with the simple problem of single-channel n-p elastic scattering in the 1S0 channel. The dependence of the R matrix width and level energy on the channel radius, "a" for fixed scattering length a0 and effective range r0 is determined. It is shown that these quantities have a simple pole for a critical value of the channel radius. The 3H(d,n)4He reaction cross section, analyzed with a two-channel effective field theory in the previous paper, is then examined using a two-channel, single-level R-matrix parametrization. The resulting S matrix is shown to be identical in these two representations in the limit that R-matrix channel radii are taken to zero. This equivalence is established by giving the relationship between the low-energy constants of the effective field theory (couplings and mass) and the R-matrix parameters (reduced width amplitudes and level energy). An excellent three-parameter fit to the observed astrophysical factor S is found for "unphysical" values of the reduced widths.

nucl-th↗

arXiv2012

Leading Relativistic Corrections to the Kompaneets Equation

We calculate the first relativistic corrections to the Kompaneets equation for the evolution of the photon frequency distribution brought about by Compton scattering. The Lorentz invariant Boltzmann equation for electron-photon scattering is first specialized to isotropic electron and photon distributions, the squared scattering amplitude and the energy-momentum conserving delta function are each expanded to order v^/c^4, averages over the directions of the electron and photon momenta are then carried out, and finally an integration over the photon energy yields our Fokker- Planck equation. The Kompaneets equation, which involves only first- and second-order derivatives with respect to the photon energy, results from the order v^2/c^2 terms, while the first relativistic corrections of order v^4/c^4 introduce third- and fourth-order derivatives. We emphasize that our result holds when neither the electrons nor the photons are in thermal equilibrium; two effective temperatures characterize a general, non-thermal electron distribution. When the electrons are in thermal equilibrium our relativistic Fokker-Planck equation is in complete agreement with the most recent published results, but we both disagree with older work.

astro-ph.CO↗

arXiv2011

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.

physics.plasm-ph↗

arXiv2009

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.

physics.plasm-ph↗

arXiv2008

Temperature Equilibration Rate with Fermi-Dirac Statistics

We calculate the electron-ion temperature equilibration rate in a fully ionized, weakly to moderately coupled plasma, using an exact treatment of the Fermi-Dirac electrons. The temperature is sufficiently high so that the quantum-mechanical Born approximation to the scattering is valid. At the heart of this calculation lies the method of dimensional continuation, a technique that we borrow from quantum field theory and use in a novel fashion to regulate the kinetic equations in a consistent manner. We can then perform a systematic perturbation expansion and thereby obtain a finite first-principles result to leading and next-to-leading order. Unlike model building, this systematic calculation yields an estimate of its own error and thus prescribes its domain of applicability. The calculational error is small for a weakly to moderately coupled plasma, for which our result is nearly exact. It should also be emphasized that our calculation becomes unreliable for a strongly coupled plasma, where the perturbative expansion that we employ breaks down, and one must then utilize model building and computer simulations. Besides providing new and potentially useful results, we use this calculation as an opportunity to explain the method of dimensional continuation in a pedagogical fashion. Interestingly, in the regime of relevance for many inertial confinement fusion experiments, the degeneracy corrections are comparable in size to the subleading quantum correction below the Born approximation. For consistency, we therefore present this subleading quantum-to-classical transition correction in addition to the degeneracy correction.

physics.plasm-ph↗

arXiv2008

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.

physics.plasm-ph↗

arXiv2007

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^2κ_D/ 4πT is small, where κ_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.

physics.plasm-ph↗

arXiv2006

Highly Charged Ions in a Dilute Plasma: An Exact Asymptotic Solution Involving Strong Coupling

The ion sphere model introduced long ago by Salpeter is placed in a rigorous theoretical setting. The leading corrections to this model for very highly charged but dilute ions in thermal equilibrium with a weakly coupled, one-component background plasma are explicitly computed, and the subleading corrections shown to be negligibly small. This is done using effective field theory methods advocated by Brown and Yaffe. Thus, corrections to nuclear reaction rates that such highly charged ions may undergo can be computed precisely. Moreover, their contribution to the equation of state can also be computed with precision. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models in this limit.

physics.plasm-ph↗

arXiv2005

Highly charged ions in a weakly coupled plasma: an exact solution

physics.plasm-ph↗

arXiv2005

Rigorous theory of nuclear fusion rates in a plasma

Real-time thermal field theory is used to reveal the structure of plasma corrections to nuclear reactions. Previous results are recovered in a fashion that clarifies their nature, and new extensions are made. Brown and Yaffe have introduced the methods of effective quantum field theory into plasma physics. They are used here to treat the interesting limiting case of dilute but very highly charged particles reacting in a dilute, one-component plasma. The highly charged particles are very strongly coupled to this background plasma. The effective field theory proves that this mean field solution plus the one-loop term dominate; higher loop corrections are negligible even though the problem involves strong coupling. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models.

physics.plasm-ph↗

arXiv2005

dE/dx to Subleading Order in the Plasma Density

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, but it is assumed that the plasma is not strongly coupled in that the dimensionless plasma coupling parameter g= e^2 κ_D/4πT is small, where κ_D is the Debye wave number. To leading order in this coupling, dE/dx is of the generic form g^2 \ln[g^2 C]. The prefactor of the logarithm is well known. We compute the constant C under the logarithm exactly. Our result differs from approximations given in the literature, with differences in the range of about 20% for cases relevant to inertial confinement fusion experiments.

physics.plasm-ph↗

arXiv2000

Finite temperature corrections to weak rates prior to nucleosynthesis

We have reexamined the electromagnetic corrections to the weak interaction rates for the transformation of neutrons to protons, and protons to neutrons, in the early universe, before freeze-out. We derive compact expressions for these rates in terms of thermal expectation values of products of fields, and we give explicit constructions of the terms to order e^2. We disagree in several respects with results in the literature.

astro-ph↗

arXiv2000

Effective Field Theory for Highly Ionized Plasmas

We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over electrostatic potential distributions. The leading order, field-theoretic tree approximation automatically includes the effects of Debye screening. Subleading, one-loop corrections are easily evaluated. The two-loop corrections, however, have ultraviolet divergences. These correspond to the short-distance, logarithmic divergence which is encountered in the spatial integral of the Boltzmann exponential when it is expanded to third order in the Coulomb potential. Such divergences do not appear in the underlying quantum theory --- they are rendered finite by quantum fluctuations. We show how such divergences may be removed and the correct finite theory obtained by introducing additional local interactions in the manner of modern effective quantum field theories. We obtain explicit results for density-density correlation functions through two-loop order and thermodynamic quantities through three-loop order. The induced couplings are shown to obey renormalization group equations, and these equations are used to characterize all leading logarithmic contributions in the theory. A linear combination of pressure and energy and number densities is shown to be described by a field-theoretic anomaly. The effective theory allows us to evaluate very easily the algebraic long-distance decay of density correlation functions.

physics.plasm-ph↗

arXiv2000

New Use of Dimensional Continuation Illustrated by dE/dx in a Plasma and the Lamb Shift

Physical processes ranging from the Lamb shift to the energy loss dE/dx of a charged particle traversing a plasma entail processes that occur over a wide range of energy or length scales. Different physical mechanisms dominate at one or the other end of this range. For example, in the energy loss problem, soft collisions that are screened by collective effects are important at large distances, while at short distances hard collisions are important where the exact details of the single-particle interactions must be taken into account. We introduce a novel application of dimensional continuation. The soft processes dominate at all scales when the spatial dimension νis less than 3, and we use them to compute the result to leading order for ν< 3. On the other hand, the hard processes dominate at all scales for ν> 3, and we use them to compute the result to leading order for these spatial dimensions. We then explain why the sum of the analytic continuation of these disparate mechanisms yields the correct leading-order result for the physical limit at ν= 3 dimensions. After applying this new method to the energy loss problem in some detail, we then show how it also provides a very short and easy way to compute the Lamb shift.

physics.plasm-ph↗

arXiv1997

Nuclear Electron Capture in a Plasma

We consider the electron density at the position of an ion of charge Ze in a plasma under conditions approximating those in the core of the sun. Numerical calculations have shown that the plasma effects on the density, over and above the ordinary Coulomb factors that are obtained in the absence of electron-electron interactions, are well represented by a reduction factor, exp{- Z e^2 beta kappa_D }, where beta is the inverse temperature and kappa_D is the Debye wave length. Although this factor is the direct analogue of the Salpeter enhancement factor for the fusion rates in stars, the elementary considerations that establish it in the fusion case are not applicable to the determination of the electron density and the resulting electron capture rates. We show analytically, through a sum rule that leads to a well-defined perturbative approach, that in the limit of Boltzmann statistics the Salpeter factor indeed provides the leading correction. We estimate residual effects, both from Fermi statistics and from short range terms.

astro-ph↗

arXiv1997

Nuclear Reaction Rates in a Plasma

The problem of determining the effects of the surrounding plasma on nuclear reaction rates in stars is formulated ab initio, using the techniques of quantum statistical mechanics. We derive a result that expresses the complete effects of Coulomb barrier penetration and of the influence of the surrounding plasma in terms of matrix elements of well defined operators. We find that possible "dynamical screening" effects that have been discussed in the literature are absent. The form of our results suggests that an approach that relies on numerical calculations of the correlation functions in a classical Coulomb gas, followed by construction of an effective two body potential and a quantum barrier penetration calculation, will miss physics that is as important as the physics that it includes.

astro-ph↗

arXiv1996

Compton Scattering on Black Body Photons

We examine Compton scattering of electrons on black body photons in the case where the electrons are highly relativistic, but the center of mass energy is small in comparison with the electron mass. We derive the partial lifetime of electrons in the LEP accelerator due to this form of scattering in the vacuum beam pipe and compare it with previous results.

hep-ph↗