Mean Free Path Of Protons Research Articles

Spreading protons in the heliosphere: a note on cross-field diffusion effects

We study how a high-speed solar wind stream embedded in a slow solar wind affects the transport and energy changes of solar energetic protons in interplanetary space, assuming different levels of cross-field diffusion. This is done using a particle transport model that computes directional particle intensities and first order parallel anisotropies in a background solar wind generated by the magnetohydrodynamic model EUHFORIA. In particular, we consider a mono-energetic 4 MeV proton injection over an extended region located at a heliographic radial distance of 0.1 AU. By using different values for the perpendicular proton mean free path, we study how cross-field diffusion may affect the energetic particle spread and intensity profiles near a high-speed solar wind stream and a corotating interaction region (CIR). We find that both a strong cross-field diffusion and a solar wind rarefaction region are capable of dispersing SEPs efficiently, producing overall low particle intensities which can in some cases prevent the SEPs from being detected in-situ, since their intensity may drop below the detected preevent intensity levels. We also discuss how accelerated particle populations form on the reverse and forward shock waves, separated by the stream interface inside the CIR. Under strong levels of cross-field diffusion, particles cross the SI and hence both accelerated particle populations merge together.

THE INFLUENCE OF DISSIPATION RANGE POWER SPECTRA AND PLASMA-WAVE POLARIZATION ON COSMIC-RAY SCATTERING MEAN FREE PATH

The influence of the polarization state and the dissipation range spectral steepening of slab plasma waves on the scattering mean free path of single-charged cosmic-ray particles is investigated in a turbulence model, where the crucial scattering of cosmic-ray particles with small pitch-angle cosines is caused by resonant cyclotron interactions with slab plasma waves. Analytical expressions for the mean free path of protons, antiprotons, negatrons, and positrons are derived for the case of constant frequency-independent magnetic helicity values ? and different values of the dissipation range spectral index k for characteristic interplanetary and interstellar plasma conditions. The positron mean free path is not affected by the dissipation range spectral index k as these particles can only cyclotron-resonate for rigidity values larger than R 0 = mpc = 938?MV. Proton and antiproton mean free paths are only slightly affected by the dissipation range spectral index k at small rigidities R < R 0. The negatron mean free path is severely affected by the dissipation range spectral index k at rigidities smaller than R 0. At high rigidities R R 0, all particle species approach the same power-law dependence R 2?s determined by the inertial range spectral index s = 5/3. The magnetic helicity value ? affects the value of the mean free path. At all rigidities, the ratio of the antiproton to proton mean free paths equals the constant (1 + ?)/(1 ? ?), which also agrees with the ratio of the negatron to the proton and positron mean free paths at relativistic rigidities. At relativistic rigidities the positron and proton mean free paths agree, as do the negatron and antiproton mean free paths.

Detecting the widths of shock fronts preceding coronal mass ejections

The perturbed zones and shocks preceding coronal mass ejections (CMEs) are studied using the data of the Mark 4, LASCO C2, and LASCO C3 coronagraphs. Detection of the perturbed zone indicating the presence or absence of the shock is most reliable in a frame moving with the frontal structure of the CME. The ability to correctly measure the width δF of the shock front using the Mark 4 and LASCO C2 data is established. The front width δF observed along the streamer belt at distances R < 5 R⊙ from the center of the Sun is of the order of the mean free path of protons. This means that the energy dissipation in the shock front is collisional at such distances. At distances R ≥ (10 − 15) R⊙, a new discontinuity with a front δ*F ≪ δF is formed in the leading portion of the front. Within the errors, δ*F ≈ (0.1–0.2) R⊙ is independent of the distance R and is determined by the LASCO C3 spatial resolution. Initially, the discontinuity on the scale δ*F is weak and coexists with the front with width δF. The relative amplitude of this discontinuity increases and the brightness profile behind it flattens as long as the distance R increases. This transformation of the brightness profile from a front of width δF to a discontinuity of width δ*F ≪ δF is explained as a transition from a collisional to a collisionless shock.

Simulated performance of the calorimetric electron telescope (CALET) experiment

CALET is a detector planned to be on-board the Japanese Experiment Module Exposed Facility (JEM-EF) of the International Space Station. The CALET mission aims at revealing unsolved problems in high energy phenomena of the Universe by carrying out a precise measurement of the high energy electrons in 1 GeV–20 TeV, the gamma-rays in 20 MeV to a few TeV and the nuclei in a few 10 GeV–1000 TeV. The main detector is composed of imaging calorimeter (IMC), total absorption calorimeter (TASC), silicon pixel array (SIA) and anti-coincidence detector (ACD) to detect various kinds of particles in very wide energy range. The total absorber thickness is 31 radiation lengths for electromagnetic particles and 1.4 interaction mean free paths for protons. Monte Carlo simulation study has been carried out for optimization of the detector performance in observing each kind of particles. We obtained following performance about the observation of very high energy (>100 GeV) electrons, which is a main target of the CALET experiment: (1) Effective geometrical factor is about 7000 cm 2 sr. (2) Energy resolution is better than a few %. (3) Angular resolution is better than 0.1°. (4) Proton rejection power is ∼10 5 with the electron detection efficiency better than 95%. We also present the simulated performance of the CALET experiment in observing other particles.

The effects of thermal conduction on the ADAF with a toroidal magnetic field

The observation of the hot gas surrounding Sgr $A^*$ and a few other nearby galactic nuclei imply that electron and proton mean free paths are comparable to the gas capture radius. So, the hot accretion flows is likely to proceed under week-collision conditions. Hence, thermal conduction has been suggested as a possible mechanism by which the sufficient extra heating is provided in hot ADAF accretion disks. We consider the effects of thermal conduction in the presence of a toroidal magnetic field in an advection-dominated accretion flow around a compact object. For a steady-state structure of such accretion flows a set of self-similar solutions are presented. We find two types solutions which represent high and slow accretion rate. They have different behaviors with saturated thermal conduction parameter, $\phi$.

Mean free path of protons and neutrons in isospin-asymmetric nuclear matter

We calculate the mean free path of neutrons and protons in symmetric and asymmetric nuclear matter, based on microscopic in-medium nucleon-nucleon cross sections. The latter are obtained from calculations of the $G$ matrix including relativistic ``Dirac'' effects. The dependence of the mean free path on energy and isospin asymmetry is discussed. We conclude by suggesting possible ways our microscopic predictions might be helpful in conjunction with studies of rare isotopes.

A spallation neutron source based on Pb target surrounded by U blanket

A new spallation source, efficient for transmutation experiments, was designed and constructed at the Dubna High Energy Laboratory (LHE). The spallation source has a cylindrical shape Pb target surrounded by natU rods. Experiments with protons of 0.7–2 GeV were performed and neutron spatial distribution on the surface of U blanket was studied. Total neutron fluences and estimates of their energy distributions were determined using solid state nuclear track detectors. Slow and fast neutron components were studied as a function of the proton beam energy. The experimental results were fitted and compared with calculations derived from empirical relations based on physics near high-energy accelerators. The results show that neutron spatial distribution along the U blanket surface (parallel to the beam direction) has the same shape independent of the proton beam energy. The neutron fluence spatial distribution is characterized by an increase at the beginning of the target and after reaching a maximum drops as a function of the target thickness. The maximum is reached at about one mean free path of protons in the Pb target. The total number of neutrons produced, as was measured on U blanket surface, is an increasing function of the proton beam energy.

Neutron yields from massive lead and uranium targets irradiated with relativistic protons

Long-lived isotopes can be transmuted into stable or short-lived elements either by neutron captures or neutron induced fission. The need of a large excess of neutrons has led to the use of accelerator driven sources (ADS). A series of experiments were carried out at the Synchrophasotron/Nuclotron of the Joint Institute for Nuclear Research (JINR) Dubna, using protons of 1.0 GeV. Solid Lead and Uranium targets surrounded by paraffin moderator were irradiated. On the outer surface of the moderator a number of Solid State Track Detectors were placed to monitor neutron spatial distribution. The results showed that the maximum neutron production was reached within the range of one to two proton mean free paths in the target. Then decreasing neutron production follows the proton beam attenuation along the target. Moreover, the results showed both targets neutron production evolution along the target, to be the same. However, neutron flux per incident proton is depended on the target mass, which was found to be higher for the heavier target.

Transparency of nuclei and mean free path of protons and pions in nuclear matter at intermediate energies

In the second resonance region of photon energies, the differential yields of neutral and charged pions are measured in the (γ, πp) reactions on Li, C, and Al nuclei versus the proton energy and the azimuthal angle of pion emission. These experimental data are analyzed on the basis of a model that takes into account both single and double quasifree pion photoproduction. This results in deriving the mean free paths of protons and neutral and charged pions and in estimating the transparency of the participant nuclei.

Propagation of Solar Neutron-Decay Protons near the Earth.

A Monte Carlo simulation of solar neutron-decay protons is performed using a simple interplanetary magnetic field (slab model) in interplanetary space. The time profile of solar neutron-decay protons obtained by our simulation is compared with observations. It is shown that the simple model can predict coherent pulses at the start of events. Magnetic field parameters used in the comparison can suggest the mean free path of protons near the Earth. The values are discussed in relation to other published results. Also, the comparisons show that it is difficult to determine the angular distribution of solar neutrons emitted at a flare site as long as the presently available solar neutron-decay protons are used.

Anomalous Mass Number Dependence of Nuclear Transparency

Abstract We examine the target mass number ( A ) dependence of the nuclear transparency calculated for ( e , e ′ p ) reactions. Generally, the transparency is proportional to A − 1 3 for large A 's and has weaker A -dependence as A decreases. The conventional nuclear physics calculation yields a transparency whose A − 1 3 dependence is reached in rather light nuclei (around A = 20). If either the proton mean-free path in nuclei becomes substantially longer, or the internal structure of the proton is explicitly incorporated in the calculation, however, the A − 1 3 dependence is reached only in extremely heavy nuclei. The A -dependence should thus serve as a signature of the so-called color-transparency phenomenon.

Anomalous mass number dependence of nuclear transparency

We examine the target mass number ( A) dependence of the nuclear transparency calculated for ( e, e′ p) reactions. Generally, the transparency is proportional to A − 1 3 for large A's and has weaker A-dependence as A decreases. The conventional nuclear physics calculation yields a transparency whose A − 1 3 dependence is reached in rather light nuclei (around A = 20). If either the proton mean-free path in nuclei becomes substantially longer, or the internal structure of the proton is explicitly incorporated in the calculation, however, the A − 1 3 dependence is reached only in extremely heavy nuclei. The A-dependence should thus serve as a signature of the so-called color-transparency phenomenon.

Proton and electron mean free paths: The Palmer consensus revisited

We present experimental and theoretical evidence suggesting that the mean free path of cosmic-ray electrons and protons may be fundamentally different at low to intermediate (less than 50 MV) rigidities. The experimental evidence is from Helios observations of solar energetic particles, which show that the mean free path of 1.4 MV electrons is often similar to that of 187 MV protons, even though proton mean free paths continue to decrease comparatively rapidly with decreasing rigidty down to the lowest channels (about 100 MV) observed. The theoretical evidence is from computations of particle scattering in dynamical magnetic turbulence, which predict that electrons will have a larger mean free path than protons of the same rigidity. In the light of these new results, 'consensus' ideas about cosmic-ray mean free paths may require drastic revision.

Interplanetary transport of solar electrons and protons: Effect of dissipative processes in the magnetic field power spectrum

Quasi‐linear theory describing charged particle transport in interplanetary space within the framework of a slab turbulence picture was for a long time confronted with the problem that the theoretically predicted mean free path for scattering at magnetic field fluctuations was too small when compared with the corresponding parameter derived from fits to observed intensity and anisotropy profiles of solar energetic particles. The theory up to now has neglected the dispersiveness of some of the scattering plasma waves and the effects resulting from the finite temperature of the plasma through which the particles propagate. We have therefore attempted to give a more realistic model of an observed interplanetary turbulence spectrum. The most simple picture we find requires the dissipation range to be constituted by parallel dispersive whistler, electron and ion cyclotron waves in a warm plasma (β ≈ 1). The dispersion relation of heavily thermally affected ion cyclotron waves needed in this model is calculated for the first time. The model is fitted to the turbulence spectrum measured on June 7, 1980, by ISEE 3 (ICE). The derived model parameters are used in a quasi‐linear calculation of both proton and electron mean free paths. As a first step resonance broadening due to wave damping is neglected. The results are compared with typical empirical proton mean free paths and with electron mean free paths obtained from fits to electron intensity and anisotropy profiles observed simultaneously by the same satellite. In both cases the theoretical values seem to be systematically larger than the empirical ones. Thus scattering enhancements by nonlinear or thermal resonance broadening or oblique waves now bear the hope to remove the discrepancy between theory and observation.

Laser effects on proton energy loss in metals

We study the influence of a strong laser field on the stopping power and the inverse mean free path of protons moving in a degenerate electron gas. The energy-loss function is derived by means of a semiclassical approximation for the laser electromagnetic field, and the random-phase-approximation formalism is used taking into account the laser effects. The contributions to the energy losses due to plasmon and electron—hole excitations are discussed in terms of photon absorption or emission processes. These effects are analyzed as a function of the proton velocity and for different frequencies and intensities of the laser field.

Injection and diffusive transport of suprathermal through energetic solar flare protons (35 keV to 20 MeV)

We have investigated the injection and interplanetary propagation of low‐energy protons that originated in a prompt solar particle event on July 20, 1981. The event was highly unusual in that solar flare protons could be seen from suprathermal energies (35 keV) to the energetic particle range (20 MeV). The observations were made in interplanetary space using the low‐energy ion instrument (DFH) and ULEWAT instrument on ISEE 3. At the higher energies, the appearance of the time‐intensity and time‐anisotropy profiles in this event were characteristic of diffusive particle propagation; however, owing to extremely quiet interplanetary conditions, it was possible to observe solar particles down to proton energies well below previous studies. We were able to fit the observed time‐intensity and time‐anisotropy profiles over the entire energy range using a model based on the spherically symmetric Fokker‐Planck equation including convection, diffusion, and adiabatic deceleration. From our model fits we find that (1) the radial interplanetary diffusion coefficient K increases with heliocentric radius r as K = K0 rb, where b is close to 1; (2) the scattering mean free path for protons, λ, increases with particle rigidity P as λ ∝ P(0.22±0.03) over the range between 9 and 160 MV; and (3) at Earth orbit, λ values lie between 0.02 AU (for ∼0.5‐MeV electrons) and 0.17 AU (for protons, 10–20 MeV). Anisotropies in this event are long lasting (&gt;48 hours) owing in part to an extended injection: the lower the energy, the longer the injection lasts. The extended period of injection appears to be evidence for diffusive coronal shock acceleration of protons during this event. Following the solar particle event maximum of intensity, a bidirectional streaming event was observed; during this period the particle anisotropies along with changes in the interplanetary magnetic field give evidence for the passage of a magnetic cloud by ISEE 3.

Proton mean-free path in nuclear matter and in finite nuclei

The mean-free path of protons is calculated in nuclear matter and in finite nuclei using the extended Skyrme interaction. The Green's function technique is employed for infinite nuclear matter to carry out the calculations analytically. The connection to finite nuclei is established and results are compared to data extracted from reaction cross sections and optical-potential fits for three closed-shell nuclei. Fixing the radius parameter as in the interpretation of the measurements leads to reasonable agreement within the accuracy of the data.

The mean free path of protons in nuclei and the nuclear radius

We determine the mean free path of protons in nuclei in the energy range 40–1000 MeV. We find that it is necessary to use in the calculation of the mean free path the nuclear radius R which reproduces the reaction and total cross sections consistently and that this radius leads to a rather small mean free path which is comparable with the value obtained in the microscopic calculation in the whole energy region.

One- and two-proton inclusive spectra in 800 MeV proton-nucleus collisions and the mean free path of protons in nuclei

One- and two-proton inclusive spectra have been measured in collisions of 800 MeV protons with C, NaF, KCl, Cu, and Pb targets. The single proton inclusive yield increases monotonically with target mass, while the two-proton yield at θ lab = ±40° associated with pp quasi-elastic scatterings shows a maximum at a mass number of about 50. A model calculation reproduces the observed target mass dependence with a mean free path of ≈2.4 fm for 800 MeV protons inside the nucleus.

The entry of solar protons over the polar caps

Observations of solar protons at energies from 1 MeV to 360 MeV are examined in relation to the information that these particles give about the magnetosphere, magnetotail and magnetopause. Trajectory integrations in a realistic model of the geomagnetic field out to 25 R E and a tail field model fitted to observations from 15 R E to 80 R E are used to obtain a better understanding of the particle motion. The mean free path of protons in the tail is found to be 700 R E and 200 R E for 100 MeV and 1 MeV protons respectively, which indicates that trajectory calculations in a static field model are valid. Structure over the polar caps at low altitudes due to interplanetary anisotropies was observed for protons > 30 MeV during the solar flares of November 18th 1968 and February 25th 1969. Apart from an easily explained direct impact zone structure, fluxes corresponding to peak anisotropic interplanetary intensity were observed to come from deep in the magnetotail. A magnetopause model of the generalised rotational discontinuity type, with a diverging tail field, is proposed and it is shown that this allows particle access into the tail with conservation of the distribution function. Particles from the direction of maximum flux (usually the Parker spiral direction) reverse their direction of motion during multiple magnetopause crossings. They eventually stay in the tail with small pitch angles and are thus observable at low altitudes. Observations show that 1 MeV protons become isotropic at the magnetopause. It is suggested that this is due to irregularities in the magnetopause, possibly caused by Kelvin Helmholtz instabilities, which are of comparable dimensions to the Larmor radius of these particles. Intensity differences over the polar cap of ▪40 per cent are expected due to the overall radial intensity gradient, and rapid local gradients can produce even greater differences. It is proposed here that sharp local intensity changes bounded by tangentional discontinuities, which convect past the Earth with the solar wind account for most of the observed polar cap intensity variations for 1 MeV protons. Anisotropies in flux produce gradients across the tail which can also be observed over the polar caps. Particle trajectories crossing the neutral sheet are analysed, and it is shown that dispersion of trajectories produces broadening of sharp interplanetary intensity changes when observed in the tail, not by a diffusion process, but through different trajectory lengths. Results of trajectory integrations at three energies are presented. These can be used to analyse polar cap structure in future work. Results of nonadiabatic particle motion in the pseudo-trapping region are shown. This motion produces effects similar to strong pitch angle scattering although it takes place in a static field.