Study of cosmic rays in the solar environment Final report, 12 Jan. 1968 - 11 Jan. 1971

Convection-diffusion equation for closed formulation of cosmic ray transport theory in solar environmen

Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed

Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained

The GRAAL high resolution BGO calorimeter and its energy calibration and monitoring system

We describe the electromagnetic calorimeter built for the GRAAL apparatus at the ESRF. Its monitoring system is presented in detail. Results from tests and the performance obtained during the first GRAAL experiments are given. The energy calibration accuracy and stability reached is a small fraction of the intrinsic detector resolution.Comment: 19 pages, 14 figures, submitted to Nuclear Instruments and Method

Planck LFI flight model feed horns

this paper is part of the Prelaunch status LFI papers published on JINST: http://www.iop.org/EJ/journal/-page=extra.proc5/jinst The Low Frequency Instrument is optically interfaced with the ESA Planck telescope through 11 corrugated feed horns each connected to the Radiometer Chain Assembly (RCA). This paper describes the design, the manufacturing and the testing of the flight model feed horns. They have been designed to optimize the LFI optical interfaces taking into account the tight mechanical requirements imposed by the Planck focal plane layout. All the eleven units have been successfully tested and integrated with the Ortho Mode transducers.Comment: This is an author-created, un-copyedited version of an article accepted for publication in JINST. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at 10.1088/1748-0221/4/12/T1200

Upadacitinib: One More Option in the Treatment of Patients with Rheumatoid Arthritis and Crohn's Disease

Arthritis and IBD are conditions that can occur in the same patient simultaneously. The complexity in managing these cases lies in detecting the signs and symptoms that point to the onset of the disease at an early stage, and in choosing an appropriate course of treatment to control the joint and intestinal aspects at the same time. In recent times, a new class of drugs has been added to the treatment options: JAK inhibitors (JAKi), of which Upadacitinib is one. Being able to manage and follow up with these patients in joint gastro-rheumatology outpatient clinics, where professionals from both disciplines are able to follow these cases appropriately, avoiding delays in diagnosis andtreatment, is also importan