Jacob Neufeld

CALCULATION OF RADIATION DOSE FROM PROTONS AND NEUTRONS TO 400 Mev

1. THIS report is a part of a continuing reappraisal of the meaning and calculation of the dose due to high energy neutrons and protons in tissue. Estimates of such dose are given in the report of Committee IV (1953-1959) of the International Commission on Radiological Protection.(l) The estimates of Committee IV, based on the work of NEARY and MULVEY,@) utilized the best experimental and theoretical data which were available at that time. Within the last few years, however, a considerable amount of new information has been obtained which permits a more detailed study of interactions of high-energy neutrons or protons with tissue. Also, new techniques have been developed to describe typical histories of neutrons or protons within a tissue phantom. In this report, revised estimates of dose and dose equivalent in tissue are given for neutrons and protons with energies up to 400 MeV.

Calculation of radiation dose due to protons and neutrons with energies from 0.4 to 2.4 GeV.

Estimates of the distribution of absorbed dose and dose equivalent with depth in a tissue slab have been made for irradiation by normally incident and also isotropically incident protons and neutrons with energies up to 2.0 GeV. The Monte Carlo calculations, based on a simplified model for nuclear interactions, take into account the production of pions as well as nucleons in nuclear interactions. The energy deposited due to ionization by charged particles is separated into LET ranges permitting different quality factors to be used. The total dose is broken down to show the contribution due to ionization by primary particles (in the case of incident protons), ionization by secondary particles, ionization by pions, excitation of residual nuclei following cascades, and the contribution from pions that stop within the tissue. Results are presented in the form of graphs showing the distribution of absorbed dose and dose equivalent with depth within the phantom for incident energies 0.6, 1.0, and 2.0 GeV. The results appear to be in reasonable agreement with experimental results. There is a rapid buildup of dose near the surface and then a more gradual buildup in the remainder of the 30 cm thick tissue slab. Pions are found to contribute less than 10% of the total dose. For normally incident neutrons, the quality factor decreases from near 10 at the surface from which the neutrons are incident to approximately 2.5 near the back of the slab.

Excitation of Hydromagnetic Waves by a Gyrating Proton Stream

It is shown that hydromagnetic waves excited by a stream of protons gyrating around the lines of a static magnetic field (helical proton beam) result from superluminous and counterstreaming instabilities. Physical conditions under which hydromagnetic P and B instabilities can occur are investigated with particular reference to the intensities of the helical proton beam and the rate of growth of the excited waves. It is found that in some instances the qualitative behavior of instabilities is different for different beam intensities. When the beam is very tenuous, the hydromagnetic B instability has a lower rate of growth than the P instability. However, for larger beam intensities the B instability has the larger rate of growth. Therefore it represents the dominant instability. The applicability of the results of the investigation to the analysis of low frequency pulsations of the terrestrial magnetic field is discussed.

On the Behavior of Plasma at Ionic Resonance

An electromagnetic wave having its wave vector parallel to the direction of the steady magnetic field Ĥ is attenuated in plasma very effectively when the frequency ω is equal to the ionic resonance frequency Ωg of the plasma. A small localized periodic disturbance initiated in a plasma in thermodynamic equilibrium at t = − ∞ and having frequency ω = Ωg produces along the direction of the magnetic field a wave motion characterized by a complex wave vector k ∼ (Ω0Ωg/c2u0i) ⅓ (√3 + i) where Ω0 is the Langmuir frequency and u0i is the mean thermal velocity of the ions in the plasma. The attenuation per wavelength at the resonance frequency is substantial since Imk/Rek = 1/√3. However, the attenuation per unit of length is not at maximum at ionic resonance since it increases for increasing frequencies when ω passes through the resonance. This is shown by the fact that for ω = Ωg we have Im(dk/dω) > 0 since at resonance Im(dk/dω) = K1/u0i + (K2/u02ui0) ⅓ where K1 and K2 are appropriate positive constants and u0...

REVISED FORMULATION OF THE KINETIC PLASMA THEORY.

Using the Maxwellian macroscopic approach and analysing the formulation of the dielectric constant, it is shown that the concept of energy has not been properly incorporated into the current kinetic plasma theory. The difficulties are due to the Boltzmann collisional term (∂F/∂t)coll which accounts for a change in the velocity distribution due to collisions alone. If one attempts to rephrase the Boltzmann-Vlasov theory in terms of the Maxwcllian macroscopic formulation, one obtains an expression for energy which is not consistent with the meaning of this concept in generalized dynamics. In a revised version developed in this analysis the Boltzmann collisional term has been eliminated and an appropriate collisional operator is introduced which is believed to describe more adequately collisional processes in a plasma. It is assumed that the collisional operator can be applied directly to the electrical intensity of the field interacting with the plasma and is effective in transforming the intensity in a col...

HYDROMAGNETIC INSTABILITIES CAUSED BY A GYRATING PROTON STREAM

EXTENSIVE literature published in recent years concerns the generation of very-low-frequency hydromagnetic waves in the Sun–Earth environment. These waves often appear at the Earths surface as regular pulsations in the continuous record of the terrestrial magnetic field variations. The period of these pulsations may extend from a fraction of a second to several minutes1.

EFFECTS OF PHANTOM GEOMETRY ON DOSE DISTRIBUTION

Calculations have been made of the spatial distribution of dose and dose equivalent due to protons of energies 250 MeV and 400 MeV incident on a tissue phantom which has dimensions approximating those of a human torso and has the form of a right elliptical cylinder with a height of 70 cm and with semiaxes of the elliptical base as 20 cm and 10 cm. The results obtained have been compared with the corresponding data previously obtained for a tissue slab having thickness of 30 cm. It is shown that within the limits of accuracy due to statistical fluctuations the distribution of dose and dose equivalent are not substantially different in a cylindrical phantom from the corresponding values in a slab phantom.

CALCULATION OF RADIATION DOSE DUE TO HIGH-ENERGY PROTONS

Abstract The work reported here represents some of the results obtained in a continuing program of the study of the dosimetry of high-energy protons and neutrons. Studies in high-energy proton dosimetry are of interest in assessing the potential radiation hazards for manned space flight and are also of interest for radiological protection in the vicinity of high-energy accelerators and for biological irradiation experiments. The present calculations consider the dose deposited in tissue by protons with energies from 400 MeV to 2 GeV. Some of the results dealing with the dose due to protons with energies up to 400 MeV have been reported previously. (1,2) For proton energies below 400 MeV, the production of pions in the cascade process was not sufficiently common to be considered significant. However, in the present calculations it is necessary to take pions into account. The basic quantity of interest in dosimetry is the absorbed dose, defined in units of the rad where 1 rad is equal to 100 ergs/gram. In order to calculate the dose equivalent, one specifies a quality factor (QF) which is often related to the values of linear energy transfer (LET) at which the energy deposition takes place. This QF-LET relationship is then used to determine the dose equivalent. The tissue phantom is the same as used previously and has the form of a slab 30 cm thick and infinite in lateral extent. The protons are assumed to be normally incident on one surface of the tissue slab. The slab is divided into 30 sub-slabs, each of which is 1 cm thick and the dose and dose equivalent in each of the sub-slabs is calculated. The Monte Carlo technique has been used in writing a code for the CDC-1604 computer to obtain the present estimates of absorbed dose and dose equivalent. The calculations have been simplified considerably by using a simpler model for the nuclear interactions than was used in the calculations up to 400 MeV. The straight-ahead approximation is used in this report (i.e. the nucleons emitted in the cascade process are assumed to have the same direction as the incident nucleon which initiates the cascade). The validity of the straight-ahead approximation has been considered at 400 MeV by Alsmiller et al. (3) and found to give good agreement with more refined methods. It is expected that the straight-ahead approximation is even better at higher energies. Much of the statistical information concerning products of the cascade such as the average number and energy distribution of emitted protons, neutrons, and pions, excitation of the residual nucleus, etc. is obtained from Metropolis et al. (4) The details of the calculations will be described further in Part II of this investigation. As new statistical information becomes available, it can easily be incorporated into the program. The estimates of dose equivalent are made on the basis of the QF-LET relationship endorsed by the International Commission on Radiological Protection (ICRP) for long-term occupational exposure. The information regarding nuclear interactions that is currently available is very incomplete and it has been necessary to make several assumptions and compromises due to the lack of sufficient experimental data. Therefore, the results presented here are preliminary and are expected to be refined when new data are available. The program runs rapidly and can process 1000 incident particles in approximately 3 min on the CDC-1604 computer.

Interaction of a Stationary Plasma with an Electron Beam

This investigation deals with a plasma‐beam system in which an electron beam of small intensity interacts with a stationary plasma immersed in a magnetic field. Expressions are derived for frequencies and rates of growth of the transverse waves excited by the beam. It is shown that the rate of growth attains a maximum value for a beam velocity β = βm, and a relationship is formulated between the quantity βm and appropriate parameters characterizing the stationary plasma. An analysis is given of the behavior of the plasma‐beam system in the neighborhood of ion gyroresonance. This investigation applies to all velocities of the electron beam except those in a highly relativistic range.

Plasma‐Beam Instability in the Hartree‐Appleton Approximation

The interaction of a beam of protons of small intensity moving with velocity cβ (where c is the velocity of light) through a stationary plasma is investigated under the assumption that the beam is aligned along the direction of an impressed static magnetic field. Expressions are derived for frequencies and rates of growth characterizing the transverse waves excited by the beam and aligned along the direction parallel to that of the impressed field. It is assumed that the frequencies of the excited waves are large when compared to the proton gyrofrequency and are sufficiently high so that the motion of the plasma ions perturbed by these waves are neglected. It is shown that two waves are simultaneously excited by a beam having velocity cβ < cβmax and a relationship is obtained between βmax and the parameters charaterizing the stationary plasma.