Search

In this work, we present a new analysis method applied to revitalize permanent magnet Compton spectrometers used to measure photon energy spectra in the MeV range. The inversion of the measured electron distribution to determine the original photon distribution is achieved via a method of consistent coupled radiation transport and magnetic field mapping of the input photon spectra to the measured electron distribution. The method of linear least squares was used to perform the unfolding of the electron distribution to the initial photon spectra, without any assumptions made regarding the electron distribution. We present an application of this method to data from a nominal 19.4 MeV flash radiographic source (the first axis of the Dual Axis Radiographic Hydro-Test Facility) capable of generating 500 R @ 1 m in ∼60 ns and a medical therapy source (a Scanditronix M22, Microtron) capable of variable energies with nominal endpoints of 6, 10, 15, and 20 MeV and an output of ∼1000–2000 R/min @ 1 m. The results provide agreement between the modeled and unfolded experimentally measured photon spectra as quantified by statistical tests, from 1.5 to 20 MeV. Experimental results are presented as well as a discussion of the novel MCNP6-based simulations and methods for reconstruction of the spectra.

The best electron beam transport through a linear induction accelerator (LIA) is achieved when the beam is well centered on the magnetic axis of the focusing solenoids. Since the beam may be injected offset from, or at an angle to, the centerline, dipole magnets are usually provided as a means to steer the beam and center it. Steering may be accomplished by trial and error, but this is very time consuming, especially for accelerators with a low repetition rate for beam position measurements and dipole adjustments. This article presents a steering method requiring a minimal number of measurements and adjustments to position the beam at any desired location, including positioning on the centerline.

In this work, two compact, permanent magnet, electron spectrometers have been built to measure the electron beam energy at the Dual Axis Radiographic Hydrodynamic Test facility. Using H- and OH- anions, the spectrometers were calibrated at the Special Technologies Laboratory in Santa Barbara, California (USA). The spectrometers were mounted on a custom drift tube that allows the magnet assemblies to be translated, which increases the path length of the electrons traveling through the magnetic field and therefore increases the upper bound of the measurable electron kinetic energy. The measurable range of electron kinetic energies is between 2.8 MeV-4.1 MeV for the first spectrometer and 14.1 MeV-21.1 MeV for the second spectrometer, with an overall measurement uncertainty of 0.32%.

The image displacement instability (IDI) has been measured on the 20 MeV Axis I of the dual axis radiographic hydrodynamic test facility and compared to theory. A 0.23 kA electron beam was accelerated across 64 gaps in a low solenoid focusing field, and the position of the beam centroid was measured to 34.3 meters downstream from the cathode. One beam dynamics code was used to model the IDI from first principles, while another code characterized the effects of the resistive wall instability and the beam break-up (BBU) instability. Although the BBU instability was not found to influence the IDI, it appears that the IDI influences the BBU. Because the BBU theory does not fully account for the dependence on beam position for coupling to cavity transverse magnetic modes, the effect of the IDI is missing from the BBU theory. This becomes of particular concern to users of linear induction accelerators operating in or near low magnetic guide fields tunes.

Our team at Los Alamos National Laboratory has successfully employed Compton spectrometers to measure the x-ray spectra of intense radiographic sources, both continuous and flash. In this method, a collimated beam of x-rays incident on a convertor foil ejects Compton electrons. A collimator may be inserted into the entrance of the spectrometer to select the angular acceptance of the forward-scattered electrons, which then enter the magnetic field region of the spectrometer. The position of the electrons at the magnet's focal plane is proportional to the square root of their momentum, allowing the x-ray spectrum to be reconstructed. Two spectrometers have been fielded since 2013; a neodymium-iron-boron permanent magnet with an energy range of 500 keV to 20 MeV, and a new samarium-cobalt magnet with an energy range of 50 keV to 4 MeV. Measured spectra were produced by x-ray generating machines of various intensities (~5 rad at 1 m per 50 ns pulse to >2000 rad/min at 1 m) and different endpoints (range of 2.25 to 20 MeV). Preliminary analysis of the electron spectra produced at two different facilities with various beryllium converter foil thicknesses is presented in these proceedings.

Accurate knowledge of the x-ray spectra used in medical treatment and radiography is important for dose calculations and material decomposition analysis. Indirect measurements via transmission through materials are possible. However, such spectra are challenging to measure directly due to the high photon fluxes. One method of direct measurement is via a Compton spectrometer (CS) method. In this approach, the x-rays are converted to a much lower flux of electrons via Compton scattering on a converter foil (typically beryllium or aluminum). The electrons are then momentum selected by bending in a magnetic field. With tight angular acceptance of electrons into the magnet of ~ 1 deg, there is a linear correlation between incident photon energy and electron position recorded on an image plate. Here we present measurements of Bremsstrahlung spectrum from a medical therapy machine, a Scanditronix M22 Microtron. Spectra with energy endpoints from 6 to 20 MeV are directly measured, using a CS with a wide energy range from 0.5 to 20 MeV. We discuss the sensitivity of the device and the effects of converter material and collimation on the accuracy of the reconstructed spectra. Approaches toward improving the sensitivity, including the use of coded apertures, and potential future applications to characterization of spectra are also discussed.

The spot size of Axis-I at the Dual Axis Radiographic Hydrodynamic Test facility was reduced by 15.5% by including a small diameter drift tube that acts to aperture the outer diameter of the electron beam. Comparing the measured values to both analytic calculations and results from a particle-in-cell model shows that one-third to one-half of the spot size reduction is due to a drop in beam emittance. We infer that one-half to two-thirds of the spot-size reduction is due to a reduction in beam-target interactions. Sources of emittance growth and the scaling of the final focal spot size with emittance and solenoid aberrations are also presented.

A Compton spectrometer has been re-commissioned for measurements of flash radiographic sources. The determination of the energy spectrum of these sources is difficult due to the high count rates and short nature of the pulses (~50 ns). The spectrometer is a 300 kg neodymium-iron magnet which measures spectra in the

Neutrals desorbed from solid surfaces by electron beam impact can be ionized by the beam and trapped in the beam potential causing beam disruption. This can increase the beam diameter on radiographic bremsstrahlung targets degrading resolution. Measurements of the number and species of neutrals desorbed by impact of a 19.8 MeV, 1.7 kA, 60 ns electron beam on thin-foil targets are made in open and closed geometries. The study focuses on aluminum and graphite foil surfaces. A fast Bayard–Alpert ionization gauge measures the number of neutral molecules released, and a quadrupole mass spectrometer measures the species mix. At high beam current density, where thermal desorption due to target heating is expected, the dominant neutral species is H2O, and approximately one monolayer of desorbed gas is released. Other prominent species such as H2, CO, and CO2 are not thermally desorbed until current densities near foil destruction are approached. The observations are in agreement with a previous hypothesis based o...

Ions or ionized neutrals released from solid surfaces by electron beam impact can be accelerated and trapped in the beam potential causing beam disruption. Experiments have been performed on the DARHT-I accelerator (1.7 kA, 19.8 MeV, 60 ns) to study this phenomenon. The beam, focused to a range of diameters, was transmitted through thin targets made of various materials. The time evolution of the beam radial profile was measured downstream of the target. For low current density, the downstream-beam radial profile was time invariant as expected for a pure electron beam. At higher current density, the downstream beam was clearly disrupted during the pulse followed by a large-amplitude transverse centroid instability. Two-dimensional calculations using the Lsp particle-in-cell code show that if the space-charge-limiting ion current is allowed to flow after the target surface temperature increases by about 400 K, the main features of the experimental observations are replicated. Three-dimensional Lsp calculations show growth of the ion hose instability at a frequency close to that observed in the experiments.

An array of photon diagnostics have been deployed on a high power relativistic electron beam diode. Surface flashover of a carbon fiber velvet cathode generates a discharge from which electrons are accelerated through a 17.8 cm diode. This discharge is assumed to be a hydrocarbon mixture. A small portion of the off energy electrons accelerated during the rise and fall of the 80 ns FWHM pulse impact the beam pipe and generate a flux of 0.1–4 MeV photons. The principal objective of these experiments is to quantify the dynamics of the hard X-ray and gamma-ray flux generated in the diode region, in addition to quantifying dynamics of the visible photons generated, and the ion species of the surface discharge on the velvet cathode. A qualitative comparison of different diagnostic results are presented, which include time resolved measurements with X-ray PIN diodes, a PMT, and CCD images. In addition initial visible spectroscopy measurements will also be presented.

An array of photon diagnostics have been deployed on a high power relativistic electron beam diode. Surface flashover of a carbon fiber velvet cathode generates a discharge from which electrons are accelerated through a 17.8 cm diode. This discharge is assumed to be a hydrocarbon mixture. A small portion of the off energy electrons (1–3 MeV) accelerated during the rise and fall of the 80 ns FWHM pulse impact the beam pipe and generate a Bremsstrahlung spectrum of 0.1–3 MeV photons. The principal objective of these experiments is to quantify the dynamics of the hard X-ray and γ-ray flux generated in the diode region, in addition to quantifying dynamics of the visible photons generated, and the ion species of the surface discharge on the velvet cathode. A qualitative comparison of different diagnostic results are presented, which include time resolved measurements with X-ray PIN diodes, a PMT, and CCD images. In addition initial visible spectroscopy measurements will also be presented.

Summary form only given. Explosive emission cathode studies are currently being conducted on a high power relativistic electron beam diode. A black velvet cathode is driven with a 75 Ohm graded transmission line which provides a 3.8 M V, 60 ns (FWHM) pulse across a fixed A-K gap of 17.5 cm. Cathode sizes range from 1.9-7 cm with space-charge limited currents of 0.26-3 kA. The principal objective of these experiments is to quantify the current emission limits and the dynamics of the gap closure process. A qualitative comparison of experimental and calculated results are presented, which include time resolved current density distributions, impedance and perveance curves and plasma expansion velocity.

An inverse Compton scattering diagnostic is currently being developed for an 80 ns, intense relativistic electron bunch with an energy of 19.8 MeV and nominal current of 1.7 kA. The principal purpose of this diagnostic is to provide a measurement of the 6-D phase space distribution of the electron beam in a single shot without disrupting its axial propagation. The electron beam is intercepted by 450 mJ of green light, which is upscattered into the soft X-ray range by the relativistic electrons. The diverging, scattered photons are diffracted onto an X-ray framing camera by an X-ray crystal concentric to the beam pipe utilizing an elongated von Hamos geometry [1]. The experimental configuration is presented, which includes the electron and photon interaction dynamics, crystal design, X-ray framing camera design, and the expected time resolved longitudinal and transverse distributions.

Summary form only given. DARHT is the dual axis radiographic hydrodynamic test facility at Los Alamos National Laboratory. The radiographic spot size is a critical parameter in the performance of the facility to produce quality radiographs. Images of the radiographic spot of the first axis of the DARHT facility have been acquired using a pinhole geometry, scintillator, and CCD framing cameras. The experimental setup, data acquisition and analysis of the time integrated radiographic spot size will be presented.

Experimental results for a high‐brightness electron‐beam source are compared to results of numerical and analytic calculations. The 4‐MV, 5‐kA beam is generated from a velvet cathode and focused by a solenoidal magnet. Data for the diode impedance and the beam focusing length and spot size agree well with numerical simulations. The minimum spot size is consistent with a normalized Lapostolle emittance of 0.12 cm rad, yielding a brightness of 3.5×108 A/m2 rad2 . Transverse beam oscillations are observed in streak photographs and are thought to be caused by electromagnetic dipole modes in the diode cavity. The oscillation amplitude is significantly reduced by making the current rise more slowly.

Surface flashover of a carbon fiber velvet cathode generates a discharge from which electrons are relativistically accelerated to γ ranging from 4.9 to 8.8 through a 17.8 cm diode. This discharge is assumed to be a hydrocarbon mixture. The principal objective of these experiments is to quantify the dynamics over the ∼100 ns pulse of the plasma discharge generated on the surface of the velvet cathode and across the anode-cathode (A-K) gap. A qualitative comparison of calculated and measured results is presented, which includes time resolved measurements with a photomultiplier tube and charge-coupled device images. In addition, initial visible spectroscopy measurements will also be presented confirming the ion species are dominated by hydrogen.

The Dual-Axis Radiographic HydroTest (DARHT) Facility is being designed to produce high-resolution flash radiographs of hydrodynamics experiments. Two 16- to 20-MeV linear induction accelerators (LIA), with an included angle of 900, are used to produce intense bremsstrahlung x- ray pulses of short duration (60-ns flat-top). Each accelerator has a 4- MeV electron source that injects an electron beam into a series of 250- kV induction cells. The three major pulsed-power systems are the injectors, the induction-call pulsed-power (ICPP) units, and the ICPP trigger systems, and are discussed in this paper.

Linear induction cells for the Dual-Axis Radiographic Hydrotest (DARHT) Facility have been tested to determine their high-voltage breakdown characteristics. A variety of full scale insulators were tested both in actual cells and in fixtures simulating induction cells. All insulators were constructed using cross-linked polystyrene (Rexolite). High-voltage pulses up to 550 kV were applied to the insulators using both a 60-ns pulse Blumlein and a 200-ns pulse cable Marx. Two different vacuum gaps were used in these tests, 1.46 and 1.91 cm. The tests were performed at various vacuum levels ranging from 1 x 10 -6 to 5 x 10/sup -8/ torr. Breakdown tests of the insulators were also performed with an electron beam generated in the vacuum gap through the use of a velvet emitter. The gap voltage and current were measured using calibrated E-dot and B-dot probes.

Summary form only given, as follows. A major concern for the new generation radiography facilities like DARHT and AIRIX is that ions or ionized neutrals released from solid surfaces by beam impact can be accelerated and trapped by the beam potential. This time-dependent positive-charge distribution, inside the beam channel, can disrupt the beam. Possible release mechanisms include electron induced desorption of neutrals or ions, thermal desorption due to beam-target heating, and melting or vaporization of the solid target. To study this, we have performed experiments on the DARHT first axis (1.7 kA, 20. MeV, 60ns). Here, the beam, focused to a range of diameters, is transmitted through a thin target made of various materials. The time evolution of the beam radial profile is measured downstream of the target. For low current density, the downstream-beam radial profile is time invariant as expected for a pure electron beam. At higher current density, the downstream beam radial profile is clearly disrupted during the pulse including a large transverse instability. This is indicative of ion release at the target foil. Analysis of the data indicates that the ions are formed from thermally desorbed neutrals ionized by the beam. This is buttressed by observations of substantial neutral release at beam densities above the beam disruption threshold. Measurements to identify the desorbed species are underway and the results will be presented. In addition, the results of experiments to measure the properties of the accelerated ions will be presented. The implications of these findings for the DARHT second axis will be discussed.

Summary form only given, as follows. Experiments have been performed on the first axis of the DARHT electron beam accelerator to study the effects on the beam of ion emission from surfaces struck by electrons. Calculations using the two-and three-dimensional Lsp particle-in-cell code were performed to compare with experimental results. Two-dimensional calculations, which allow the release of ions when the impacted surface temperature increases by 400 K accurately replicate experimental results showing beam blow-up downstream of the surface just after ion emission. Three-dimensional calculations show the onset of a hose instability after beam blow up in agreement with observations. The frequency of this instability indicates a large component of H/sup +/ ions, which may come from the "cracking" of desorbed water. Calculations in support of experiments to identify the desorbed species are presented.

The Relativistic Electron-Beam Experiment (REX) pulse power generator is used to produce a 4 MeV, 5 kA, 50 ns cathode. Multiple current rise times are used to examine pulse-power-induced beam oscillations. Diagnostics include a streak camera and high-speed electronic probes for monitoring current and voltage. Correlation between beam oscillations and TE-TM (transverse electric-transverse magnetic) cylindrical cavity modes in the anode-cathode (A-K) gap is examined. Electromagnetic excitation of the cylindrical A-K gap in the REX experiments was found to produce unacceptable levels of beam motion as a function of time. Correction of hardware asymmetries did not eliminate the problem; the problem was solved by tailoring the current rise time of the pulse power to minimize the coupling of the pulse power drive to the cavity. >

The Relativistic Electron-Beam Experiment injector at the Los Alamos National Laboratory is used to generate a 4-MV pulse across an anode-cathode gap. A simple metal photocathode is illuminated by a pulsed excimer laser. Time-resolved measurements of current, voltage, and current density were made. The resulting quantum efficiencies are being used to obtain the required laser power for a multikiloampere, high-brightness electron gun to be used as an injector for a linear induction accelerator. It is shown that an aluminum photocathode capable of emitting 3.3 kA would require an ArF laser operating at 650 kW/cm/sup 2/. This would generate 72 A/cm/sup 2/, and the laser energy is well below the plasma threshold. To construct a DARHT (Dual Axis Radiographic Hydrotest Facility) injector (3.3 kA, 60 ns), a 1.75-J ArF laser would be required. This type of laser is within current electron-beam-pumped laser technology. >

The REX machine at Los Alamos National Laboratory is being used to generate a 4-MV, 5-kA, 50-ns electron beam. The beam is produced by a planar velvet cathode, accelerated through a foilless anode aperture, and transported by an air core magnetic lens. Extensive measurements of the time-resolved ( >

Recent advances in time-to-digital converters (TDCs) have made 50-MHz RF phase measurement possible without the use of double-balanced mixers. These advances allow zero crossing discriminators to be used in conjunction with fast CAMAC TDCs to make amplitude-independent phase measurements. This method uses a time interval proportional to the phase angle, thus eliminating the calculations and calibration required with double-balanced mixers. The detection system is capable of accurate (+or-2 degrees ) measurement of phase angle between signals of unknown amplitude at 50 MHz. It is concluded that, in terms of simplicity, accuracy, cost, and flexibility, the method is superior to the double-balanced mixer approach previously used at the Los Alamos PHERMEX (Pulsed High Energy Radiographic Machine Emitting X-rays) facility. >

The velvet cathode material of a 4-MeV, electron beam injector was replaced with a material cathode and driven by an ArF excimer laser. Time-resolved measurements of photoelectron current and effective cathode temperature were made. A streak camera and B-dot (magnetic field) probes were the primary diagnostics for the experiment. The streak camera determined effective cathode temperature in a single spatial dimension. Time-integrated photography was used to observe plasma information in the cathode region. The results will be used to ascertain the feasibility of long-pulse (75-ns) beam generation for injection into a linear induction accelerator. >

The REX machine at LANL (Los Alamos National Laboratory) is being used as a prototype to generate a 4-MV, 4.5-kA, 55-ns flat-top electron beam as a source for injection into a linear induction accelerator of the 16-MeV dual-axis radiographic hydrotest facility. The pulsed-power source drives a planar velvet cathode producing a beam that is accelerated through a foilless anode aperture and transported by an air core magnetic lens for injection into the first of 48 linear induction cells. Extensive measurements of the time-resolved ( >

The PHERMEX (Pulsed High Energy Radiographic Machine-Emitting X-rays) electron beam accelerator at Los Alamos National Laboratory, a 50-MHz, 30-MV standing-wave device, typically operates with a 500-A, 600-kV injector. A higher-current injector is under consideration, and the authors have modeled a flat-cathode diode geometry which can deliver 1-1.5 kA. A three-coil field configuration has been designed to maintain low beam emittance in the diode region. It is shown that the existing two transport magnets are marginally capable of transporting a 1 kA beam to the first RF cavity. The authors examine the possibility of accelerating a 4-kA, 4-MV beam, which could be provided by an existing pulsed power machine, through the first RF cavity. >

Summary form only given, as follows. It is well known in the intense beam community that when an intense electron beam raises the surface temperature of a solid target (e.g., electrode or aperture) to 300-400 deg C, that loosely bound adsorbed molecules are rapidly released from the surface often followed by speedy ionization. This can lead to adverse beam or diode behavior. Less well known is that even in the absence of heating, electron induced desorption of neutrals or ions can have deleterious effects on beam dynamics. We discuss computer modeling to assess the importance of desorbed particles on beam dynamics, experimental measurements to determine the level of induced desorption, and cleaning techniques to reduce adsorbed molecules on surfaces for the DARHT-II, 2 kA, 20 MeV, 2 /spl mu/s beam.

A major concern for the DARHT second axis (2 kA, 18.6 MeV, 2000 ns) is that ions or ionized neutrals released from solid surfaces (e.g., apertures, septum, dumps, and targets) by beam impact can be accelerated and trapped by the beam potential. This positive charge will be electrically attracted to the beam and could disrupt it. To study this, experiments were performed on the DARHT first axis. Here, the beam, focused to a range of diameters, is transmitted through thin foils made of various materials. The time-dependent beam radial profile is measured downstream of the target. For low current density (depending on the material used), the downstream-beam profile is time invariant as expected. At higher current density, the downstream-beam radius changes during the pulse followed by transverse instability. Data, particle-in-cell simulations, and comparisons are presented.

We report on calculations carried out during 1990 in support of on-going and planned beam experiments at M-4. A higher-current injector for PHERMEX is under consideration and we have modeled a REX-like diode geometry which can deliver 1--1.5 kA. A three+coil focusing configuration has been designed to maintain low beam emittance in the diode region. We show that the existing two transport magnets are marginally capable of transporting a 1 kA beam to the a-cavity. This work is described in Sec. 2. In Sec. 3, we look at the possibility of accelerating a 4 kA, 4 MV beam, which could be provided by the REX machine, through the PHERMEX a cavity. Simulation results indicate that this is feasible. Because of the high cost and limited pulse length of a REX injector, however, a 1-1.5 kA upgrade is a more attractive option at this time. Computations in support of ongoing REX experiments are described in Sec. 4. We have modeled the generation of transverse beam oscillations through the excitation of an electromagnetic dipole mode in the diode cavity. Results show that oscillating magnetic fields on the order of 1--2 gauss are sufficient to cause the oscillation amplitudes observed. A simulation was carried to look at the effect of placing iron rings inside the windings of the REX anode magnet. We conclude that this causes no significant degradation of beam emittance. We have also looked at the focusing produced when the REX beam is injected into a laser-ionized plasma channel. This is a possible alternative to a magnetic lens to obtain a small spot-size. Finally, in Sec. 5, we give results of preliminary calculations of XUV and X-ray photon production through laser backscattering off a relativistic electron beam. There are plans to carry out such an experiment on REX in the near future.

The first guiding of multiple pulses from a rf accelerator by an ultraviolet‐laser‐ionized channel in low‐pressure benzene has been demonstrated. In particular, two 5‐ns, 750‐A, 30‐MeV pulses separated by 20 ns were transported a maximum distance of 13.5 m. Detailed measurements of the temporal behavior of the beam as it propagated versus distance, laser‐channel parameters, and accelerator conditions were made.

Determinations of the σ term and s-wave scattering lengths for pion-nucleon scattering are made using interior dispersion relations. The result for the σ term is obtained by extrapolating to the Cheng-Dashen point in only one variable. It is completely independent of the pion-nucleon coupling constant and insensitive to d and f waves in the resonance region. The use of interior dispersion relations allows a series of s-wave scattering length determinations to be made. It is observed that data at intermediate scattering angles gives more consistent results than data near the forward or backward directions, lending further support to the σ term calculation which utilizes only interior angle information.

A method for determining the pion-nucleon coupling constant f$sup 2$ by the application of an interior dispersion relation to the B$sup +$$pi$N scattering amplitude is presented, and its advantages over other dispersion relation techniques are discussed. The method is used to calculate f$sup 2$ for two sets of phase shifts: CERN 71 of Almehed and Lovelace and a modified version of the Carter, Bugg, and Carter solution, to obtain f$sup 2$ = (81.5 +- 1.5) x 10$sup -3$ and f$sup 2$ = (79.5 +- 1.0) x 10$sup -3$, respectively. (AIP)

Results are presented for the radiation‐induced transient darkening of thin organic polymer films normally used as Cerenkov light emissions sources. The radiation source is a 27‐MeV, 10‐μC, 200‐ns electron beam generated by the PHERMEX accelerator. The typical dose for a single pulse is 5 Mrad. At this dose, the broadband time‐resolved percent transmission above 520 nm was measured for four common polymers: polyimide (Kapton‐H), polyethylene terephthalate (Mylar), cellulose acetate, and high‐density polyethylene. Kapton was found to darken the most and polyethylene darkened the least. The recovery time to normal transmission for Kapton was found to be greater than 10–20 μs. The radiation‐induced attenuation coefficient is shown to depend on electronic band energy separation. The results show that Kapton is not the material of choice for a Cerenkov light source.

An ArF excimer laser was used to produce photoelectrons from common metal surfaces at modest vacuum. The photoelectrons are subsequently accelerated across an anode‐cathode gap. Both space‐charge and emission‐limited flow were examined. The temporal characteristics of the emission‐limited electron beam produced by this device are nearly identical to those of the laser pulse used to produce the photoemission. In the space‐charge‐limited case, a rise time of 3 ns was obtained. Maximum current densities of 70 A/cm2 were achieved.

The collision of two hemishells is analyzed where one hemishell is clamped and the other impinges on the inner surface of the clamped hemishell. A model of rigid-perfectly plastic behavior is proposed for the flow of material in the region of contact. An expression relating velocity and deformation is obtained and compared with the results of experiments.