arXiv subjects

Bernard Gottschalk

Publications and source records attributed to Bernard Gottschalk.

14 recordsLinked to original sources

arXiv2020

Measuring the length of stretched wires with a avalanche oscillator

We measure the length of stretched wire pairs by using them as the delay line pulse shaping element in an avalanche oscillator. The circuitry and method are extremely simple, and insensitive to oscillator supply voltage, to the particular transistor (2N3904) used and to wire tension. Rudimentary tests with simulated broken wires show that these can be detected easily. It remains to be seen whether the technique will work at scale with realistic wire planes, but it should be at least as good as reflecting short pulses.

physics.ins-det↗

arXiv2019

Using a 3D printer for 2D beam profile measurements in proton radiotherapy

We have used an inexpensive 3D printer mounting an inexpensive pre-irradiated silicon diode to measure the 2D dose distribution of a small (approximately 10mm FWHM) proton beam. z was measured with high resolution whereas x was changed on a 2mm grid for a total of 12 scans and 2 repeats in 20 minutes. The peak dose to the diode was approximately 530 cGy/s, and no degradation in diode sensitivity was observed. We present beam profiles and a 2D beam contour derived from these data. Most of the scan time was spent changing x by hand, and a more appropriate 3D printer along with an improved setup and printer control software would reduce that to about 1 minute for an end-to-end absolute 2D dose measurement. We propose extending this to 3D (2D transverse plus depth) for appropriate small beams by adding a small water tank.

physics.ins-det↗

arXiv2019

Rapid measurement of tension in multi-wire arrays using free damped oscillations

We explore the possibility of using free (as opposed to driven) oscillations to verify wire tension in large, open-frame multiwire planes. Using finite-element simulation we predict the signal when two wires are set in motion by applying and holding a DC voltage between them (electrostatic excitation). The resulting current signal is marginal. However, the program relates voltage, oscillation amplitude and signal, and it is easy to get enough amplitude (of order microns) by gently tapping the wire frame. We perform an end-to-end experimental test. Four 1.5m wires, at various tensions around 5N, are mounted in an aluminum channel. They are connected to a low-noise, balanced current-to-voltage preamp designed for good common-mode rejection. The 150V bias, from 9V batteries in series, is built into the preamp. Data are taken with a Tektronix 1202B scope, stored on a USB flash drive, and transferred to a laptop computer for analysis. Ten measurements, each with 2500 samples spanning 1s, are taken for each of the three wire pairs. The wires are excited by tapping the frame with a small mallet. Because the wire tensions are different, the waveforms exhibit beats. The data are analyzed by a program which decomposes the waveform step by step to extract the base and beat frequencies and thereby, two resonant frequencies per wire pair. Finally, those frequencies are disambiguated to obtain the frequency for each wire, which is then converted to a tension. The four tensions are then found mechanically by measuring the g/mm required to deflect each wire at its midpoint. The two values of tension agree well. We conclude that the method verifies tension to approximately 2% (1 sigma) in a little over 1s for 1.5m wires, and would be faster for shorter wires.

physics.ins-det↗

arXiv2018

Radiotherapy Proton Interactions in Matter

A survey of physics useful to proton radiotherapy, centered on stopping, scattering and hard scatters: 1. Introduction 2. The fundamental formula dose = fluence x mass stopping power. Practical units, comments on effective stopping power. 3. Range: experimental definition, Beth-Bloch CSDA theory, range-energy tables and approximations, range straggling. 4. Multiple Coulomb Scattering: suggested reading, elements of Moliere theory, the Gaussian approximation, scattering power. 5. Hard scatters (nuclear interactions): contributing reactions, shape and size of the halo, experiment, halo as a Monte Carlo test. 6. Bragg curve (effective stopping power): limiting cases S_em and S_mixed, transverse equilibrium, computing S_em, measuring S_mixed, parameterizing the nuclear halo. 7. Looking ahead: Fermi-Eyges theory, the Preston and Koehler rules, a proton dose algorithm from first principles. Appendices: A. Acronyms B. Symbols C. Gaussians D. Relativistic kinematics E. Simple design problems.

physics.med-ph↗

arXiv2017

Global surface temperature trends and the effect of World War II

Using parametric analysis (curve fitting) we find a persistent temperature bump, coincident with World War II (WW2), in eight independent time series, four land- and four ocean-based. We fit the data with a Gaussian on a quadratic background. Six parameters (constant, linear and quadratic background terms and the amplitude, position and width of the Gaussian) are free to vary. The mean fitted Gaussian amplitude is 0.339$\pm$ 0.065$\,^\circ$C, non-zero by 5.2$σ$ and therefore not accidental. The area is 2.0$\pm$0.5$\,^\circ$C yr. Temperature recovered to baseline rather quickly. Rather than coincidence, or systematic measuring error synchronized with WW2, we conjecture the bump is due to human activity, including the greatly increased combustion (relative to that era) of fossil and other fuels. Background surface temperature behavior, a byproduct of our study but largely independent of the WW2 bump, is far more consequential nowadays. The linear term, 0.747$\pm$0.023$\,^\circ$C/century, agrees well with other findings, but the present-day rate of increase, $\approx$2.5$\,^\circ$C/century, is far greater because of the quadratic term.

physics.ao-ph↗

arXiv2017

Global surface temperature trends and the effect of World War II: a parametric analysis (long version)

We fit 12 independent surface temperature time series (zones of latitude), 6 land- and 6 ocean-based, with a Gaussian (centered around WW2) on a quadratic background. The four polar zones are unusable. Each of the remaining 8 shows evidence of a 0.2-0.3 degree C bump, although one zone is dropped from the final analysis because of an aberrant fit. Thus, we find that a surface temperature increase around WW2 is a robust, statistically significant (5.2 sigma) feature of the data, and must either be a coincidence, due to systematic error that came and went around WW2, or direct evidence of the effect of human activity (an increase in combustion of various sorts) on the global climate. The fact that, at least in that era, the temperature recovered quickly, is encouraging. On the other hand, extrapolation of the background temperature rise predicts an increase of 0.5 degree C in the next 20 years if conditions remain the same.

physics.ao-ph↗

arXiv2016

Comparison of Geant4 multiple Coulomb scattering models with theory for radiotherapy protons

Usually, Monte Carlo models are validated against experimental data. However, models of multiple Coulomb scattering (MCS) in the Gaussian approximation are exceptional in that we have theories which are probably more accurate than the experiments which have, so far, been done to test them. In problems directly sensitive to the distribution of angles leaving the target, the relevant theory is the Moliere/Fano/Hanson variant of Moliere theory. For transverse spreading of the beam in the target itself, the theory of Preston and Koehler holds. Therefore, in this paper we compare Geant4 simulations, using the Urban and Wentzel models of MCS, with theory rather than experiment, revealing trends which would otherwise be obscured by experimental scatter. For medium-energy (radiotherapy) protons, and low-Z (water-like) target materials, Wentzel appears to be better than Urban in simulating the distribution of outgoing angles. For beam spreading in the target itself, the two models are essentially equal.

physics.med-ph↗

arXiv2016

Comprehensive proton dose algorithm using pencil beam redefinition and recursive dynamic splitting

We compute, from first principles, the absolute dose or fluence distribution per incident proton charge in a known heterogeneous terrain exposed to known proton beams. The algorithm is equally amenable to scattered or scanned beams. All objects in the terrain (including collimators) are sliced into slabs, of any convenient thickness, perpendicular to the nominal beam direction. Transport is by standard Fermi-Eyges theory. Transverse heterogeneities are handled by breaking up pencil beams (PBs) either by conventional redefinition or a new form of 2D recursive dynamic splitting: the mother PB is replaced, conserving emittance and charge, by seven daughters of equal transverse size. One has 1/4 the charge and travels in the mother's direction and six have 1/8 the charge, are arranged hexagonally and radiate from the mother's virtual point source. The longitudinal (energy-like) variable is pv (proton momentum times speed). Each material encountered is treated on its own merits, not referenced to water. Slowing down is handled by $R=a(pv)^b$ fitted to standard range-energy tables. Multiple Coulomb scattering is handled by a scattering power $T_\mathrm{dM}$ acting as a proxy for Moliere theory. We present examples from a proof-of-principle Fortran program and speculate about putting the algorithm into practice.

physics.med-ph↗

arXiv2015

Validation of nuclear models in Geant4 using the dose distribution of a 177 MeV proton pencil beam

A proton pencil beam is associated with a surrounding low-dose envelope, originating from nuclear interactions. It is important for treatment planning systems to accurately model this envelope when performing dose calculations for pencil beam scanning treatments, and Monte Carlo (MC) codes are commonly used for this purpose. This work aims to validate the nuclear models employed by the Geant4 MC code, by comparing the simulated absolute dose distribution to a recent experiment of a 177 MeV proton pencil beam stopping in water. Striking agreement is observed over five orders of magnitude, with both the shape and normalisation well modelled. The normalisations of two depth dose curves are lower than experiment, though this could be explained by an experimental positioning error. The Geant4 neutron production model is also verified in the distal region. The entrance dose is poorly modelled, suggesting an unaccounted upstream source of low-energy protons. Recommendations are given for a follow-up experiment which could resolve these issues.

physics.med-ph↗

arXiv2015

On the nuclear halo of a proton pencil beam stopping in water

The dose distribution of a pencil beam in water consists of a core, a halo, an aura and (possibly) spray. The core is due to primary protons which suffer multiple Coulomb scattering (MCS) and slow down by multiple collisions with atomic electrons (Bethe-Bloch theory). The halo is due to charged secondaries, many of them protons, from elastic interactions with H, elastic and inelastic interactions with O, and nonelastic interactions with O. We show that the halo radius is roughly one third of the beam range. The aura is due to neutral secondaries (neutrons and gamma rays). Spray denotes dose, avoidable in principle, coming in from the beam line. We have measured the absolute dose at 177 MeV using a test beam in a water tank. The beam monitor was a PPIC 'proton counter' and the field IC a dose calibrated Exradin T1. We took depth-dose scans at ten displacements from the beam axis ranging from 0 to 10 cm. The dose spans five orders of magnitude, and the transition from halo to aura is obvious. We present model-dependent (MD) and model-independent (MI) fits to these data. The MD fit has 25 parameters, and the goodness of fit (rms (measurement/fit) - 1) is 15%. The MI fit uses cubic spline fits in depth and radius. The goodness of fit is 9%. This fit is more portable and conceptually simpler. We discuss the prevalent parameterization of the core/halo originated by the PSI group. We argue that its use of T(w), a mass stopping power which includes energy deposited by nuclear secondaries, is incorrect. The electromagnetic (Bethe-Bloch) mass stopping power should be used instead. In consequence, 'Bragg peak chamber' measurements and associated corrections are, in our view, irrelevant. Furthermore, using T(w) leads to spurious excess dose on the axis of the core around midrange, which may be significant in fields involving relatively few pencil beams.

physics.med-ph↗

arXiv2014

Nuclear halo of a 177 MeV proton beam in water: theory, measurement and parameterization

The dose distribution of a monoenergetic pencil beam in water consists of an electromagnetic "core", a "halo" from charged nuclear secondaries, and a much larger "aura" from neutral secondaries. These regions overlap, but each has distinct spatial characteristics. We have measured the core/halo using a 177MeV test beam offset in a water tank. The beam monitor was a fluence calibrated plane parallel ionization chamber (IC) and the field chamber, a dose calibrated Exradin T1, so the dose measurements are absolute (MeV/g/p). We performed depth-dose scans at ten displacements from the beam axis ranging from 0 to 10cm. The dose spans five orders of magnitude, and the transition from halo to aura is clearly visible. We have performed model-dependent (MD) and model-independent (MI) fits to the data. The MD fit separates the dose into core, elastic/inelastic nuclear, nonelastic nuclear and aura terms, and achieves a global rms measurement/fit ratio of 15%. The MI fit uses cubic splines and the same ratio is 9%. We review the literature, in particular the use of Pedroni's parametrization of the core/halo. Several papers improve on his Gaussian transverse distribution of the halo, but all retain his T(w), the radial integral of the depth-dose multiplying both the core and halo terms and motivating measurements with large "Bragg peak chambers" (BPCs). We argue that this use of T(w), which by its definition includes energy deposition by nuclear secondaries, is incorrect. T(w) should be replaced in the core term, and in at least part of the halo, by a purely electromagnetic mass stopping power. BPC measurements are unnecessary, and irrelevant to parameterizing the pencil beam.

physics.med-ph↗

arXiv2014

Skewness and kurtosis as measures of range mixing in time resolved diode dosimetry

Technical Note describing studies, in 2011, of time resolved diode dosimetry in an anthropomorphic phantom at the Francis H. Burr Proton Therapy Center, Massachusetts General Hospital, Boston, MA. This technique measures the water equivalent path length (WEPL) to a diode dosimeter with sub-millimeter precision, using very little dose. It may allow one to use the proton stopping point (otherwise too uncertain) to cut between tissue to be treated and tissue to be spared, in cases (such as the prostate) where a diode can be placed in a cavity (the rectum) distal to the target. A potential problem is range mixing, where (because of scattering) protons may arrive at a diode with different energy-loss histories. The WEPL reported by such a diode is meaningless and must be ignored. We therefore use an array of diodes, of which some are likely to be at more favorable locations. In addition to the overall analysis of time resolved data, this Note describes in detail how range mixed diodes can be identified by looking at the skewness and kurtosis of the time dependent signal.

physics.med-ph↗

arXiv2012

Techniques of Proton Radiotherapy: Transport Theory

These are notes for the lecture on Transport Theory in a one-week intensive course, "Techniques of Proton Radiotherapy". Topics are: Phase space diagrams: model beam line-effect of a scatterer-effect of a drift-the beam ellipse-phase space diagrams for the model beam line-emittance change in a drift-emittance change in a scatterer-phase space for a more realistic beam line-summary Miscellaneous topics: review of Gaussians-the Gaussian approximation to multiple Coulomb scattering (MCS)-relativistic single particle kinematics-completing the square-scattering power Fermi-Eyges theory: history-the basic theory-the beam ellipse-drawing the ellipse given the moments-ellipse examples-transporting the beam ellipse through a slab-emittance change in a drift-emittance change in a scatterer-differential form of the transport equations-equivalent sources-beam contained in the beam ellipse-summary Beam spreading in matter: theory of Preston and Koehler-generalization to heavy ions-experimental tests (Preston and Koehler, Phillips, Wong et al.)-summary Analytical geometry of the ellipse (appendix): tilted ellipse-transformation to principal frame-summary and explicit procedures-area enclosed by the ellipse

physics.med-ph↗

arXiv2009

On the scattering power of radiotherapy protons

Scattering power (T = d/dx of mean squared multiple Coulomb scattering (MCS) angle), as used in proton transport theory, is properly viewed as a differential description of the Gaussian approximation to MCS theories such as Moliere's. That is, we seek a function T which, when integrated over a finite slab, will recover the Moliere/Fano/Hanson angle for that slab. To be accurate, T must include a single scattering correction, which means mathematically it must be nonlocal, depending on how much MCS has taken place as well as the energy and scattering material at the POI. We review five formulas for T and introduce a sixth, testing each against the Moliere/Fano/Hanson prediction as well as experimental data. We discuss how sensitive some practical problems are to the choice of T. That choice is probably most important for general Monte Carlo codes, which are expected to address a wide variety of problems.

physics.med-ph↗