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Showing papers in "IEEE Transactions on Nuclear Science in 1981"


Journal ArticleDOI
TL;DR: In this paper, a mathematical model for differential time-of-flight measurements in tomography systems that employ coincidence detection of the annihilation photons created with positron emitting radionuclides is developed.
Abstract: Improvements in high speed electronics and scintillation-crystal technology now permit usable differential time-of-flight measurements to be made in tomography systems that employ coincidence detection of the annihilation photons created with positron emitting radionuclides. A mathematical model for these new measurements is developed in this paper. Reconstruction algorithms and their signal-to-noise ratio performance are given.

230 citations


Journal ArticleDOI
TL;DR: In this article, the root mean square (rms) noise level in attenuation corrected images of a uniform cylindrical source was measured and found to agree with theoretically predicted vaiues obtained with the following equation: %rms = 100 (1.8)3/2? Reff Rs 1/2 Abody Cavg / 21/2Ntotal1/2(FF)1/ 2 where Reff is the effective radius of the source, RS is the actual source radius, Abody is the attenuation factor for surrounding non-source body material, Cav
Abstract: The qualitative imaging capability of single photon emission computed tomography (SPECT) using complete angular sampling has previously been demonstrated by several investigators. In order to obtain quantitative information such as absolute volumes and regional radionuclide concentrations using SPECT systems it is necessary to determine the system characteristics which contribute to the intrinsic measurement process and limit its precision. This manuscript describes some of the more important physical factors which can affect the measurement process of scintillation camera based SPECT systems and provides information concerning the type of quantitative measurements that can currently be obtained with these devices. Using our rotating camera based SPECT system the root mean square (rms) noise level in attenuation corrected images of a uniform cylindrical source was measured and found to agree with theoretically predicted vaiues obtained with the following equation: %rms = 100 (1.8)3/2 ? Reff Rs1/2 Abody Cavg / 21/2Ntotal1/2(FF)1/2 where Reff is the "effective" radius of the source, RS is the actual source radius, Abody is the attenuation factor for surrounding non-source body material, Cavg is the average attenuation correction factor for the center of the source, Ntotal is the total number of events, and FF is the algorithm filter factor and equals the integral of the square of the spatial frequency filter function. Using a semi-automatic region of interest (ROI) program and the multi-slice capability of our SPECT system, the volumes of plastic spherical sources placed inside a larger cylindrical source were measured.

223 citations


Journal ArticleDOI
TL;DR: In this article, a reconstruction algorithm for TOF-positron computed tomography (PCT) based on the back-projection with 1-dimensional weight and 2-dimensional filtering is presented.
Abstract: In positron CT, the path difference of annhilation pair gamma rays can be measured by time-of-flight (TOF) difference of pair gamma rays. This TOF information gives us rough position information along a projection line and will reduce noise propagation in the reconstruction process. A reconstruction algorithm for TOF-positron computed tomography (PCT) based on the back-projection with 1-dimensional weight and 2-dimensional filtering is presented. Also a formula to evaluate the variance of the reconstructed image and the optimal back-projection function are presented. The advantage of TOF-PCT over conventional PCT was investigated in view of noise figure. An example of such noise figure evaluations for CsF and liquid Xenon scintillators is given.

170 citations


Journal ArticleDOI
TL;DR: A very efficient back-projection algorithm which results in large time savings when implemented in machine code and a minor modification to this algorithm which converts it to a re- projection procedure with comparable efficiency is described.
Abstract: While the computation time for reconstructing images in C.T. is not a problem in commercial systems, there are many experimental and developmental applications where resources are limited and image reconstruction places a heavy burden on the computer system. This paper describes a very efficient back-projection algorithm which results in large time savings when implemented in machine code. Also described is a minor modification to this algorithm which converts it to a re-projection procedure with comparable efficiency.

137 citations


Journal Article
TL;DR: In this paper, the influence of edge focusing on the tunes and chromaticities of the NSLS rings is described and a correction to the fringe field gradient peculiar to a combined function magnet with strong edge focusing is also found.
Abstract: Beam transport matrix elements describing the linearly falling fringe field of a combined function bending magnet are expanded in powers of the fringe field length by iteratively solving the integral form of Hill's equation. The method is applicable to any linear optical element with variable focusing strength along the reference orbit. Results for the vertical and horizontal focal lengths agree with previous calculations for a zero gradient magnet and an added correction to the dispersion is found for this case. A correction to the fringe field gradient peculiar to a combined-function magnet with strong edge focusing is also found. The influence of edge focusing on the tunes and chromaticities of the NSLS rings is described. The improved chromaticity calculation for the booster was of particular interest since this ring has bending magnets with poletips shaped to achieve small positive chromaticities.

134 citations


Journal ArticleDOI
TL;DR: The basic imaging properties of the Donner 280-BGO-Crystal positron tomograph were measured and compared with the same system when it was equipped with 280 NaI(T1) crystals, which results in an overall reduction in the fraction of accidental events recorded.
Abstract: The basic imaging properties of the Donner 280-BGO-Crystal positron tomograph were measured and compared with the same system when it was equipped with 280 NaI(T1) crystals. The NaI(T1) crystals were 8 mm × 30 mm × 50 mm deep, sealed in 10 mm wide stainless steel cans. The BGO crystals are 9.5 mm wide × 32 mm × 32 mm deep and as they are not hygroscopic do not require sealed cans. With a shielding gap of 3 cm (section thickness 1.7 cm FWHM) the sensitivity of the BGO system is 55,000 events per sec for 1 ?Ci per cm3 in a 20 cm cylinder of water, which is 2.3 times higher than the NaI(T1) system. For a 200 ?Ci/cm line source on the ring axis in a 20 cm diameter water cylinder, the BGO system records 86% of the scatter fraction and 66% of the accidental fraction of the NaI(T1) system. The lower light yield and poorer time resolution of BGO requires a wider coincidence timing window than NaI(T1); however, the ability to use full-energy pulse height selection with a 2.3-fold improvement in sensitivity results in an overall reduction in the fraction of accidental events recorded. The in-plane resolution of the BGO system is 9-10 mm FWHM within the central 30 cm diameter field, and the radial elongation at the edge of the field in the NaI(T1) system has been nearly eliminated.

119 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived the thin-slot formalism in a manner compatible with the 3D EMP time-domain finite-difference code THREDII, which permits inclusion of conducting plates with arbitrarily narrow slots or gaps without requiring any corresponding need to reduce the cell size to the gap width.
Abstract: This article derives the thin-slot formalism in a manner compatible with the 3D EMP time-domain finite-difference code THREDII. The thin-slot formalism permits inclusion of conducting plates with arbitrarily narrow slots or gaps without requiring any corresponding need to reduce the cell size to the gap width. The basic concept of this formalism is to increase the effective ? seen by the electric field across the gap and to reduce, in proportion, the ? seen by the magnetic field transverse to the gap. The conducting plate and gap may be imbedded in a lossy medium, and the material on the two sides of the gap may be dissimilar.

88 citations


Journal ArticleDOI
TL;DR: In this article, the number of events in which a given threshold amount of energy is deposited in a 4.2?m detector varied with incident proton energy in a manner similar to previous measurements of the proton-induced soft error cross section.
Abstract: Measurements of the energy deposited in silicon surface-barrier detectors as a result of proton-induced nuclear reactions were carried out at the Harvard Cyclotron for protons with incident energies ranging from 50 to 158 MeV and detectors with thicknesses of 2.5, 4.2, 24.1, 100, and 200 ?m. The number of events in which a given threshold amount of energy is deposited in a 4.2 ?m detector varied with incident proton energy in a manner similar to previous measurements of the proton-induced soft-error cross section. The number of events in which at least a threshold amount of energy was deposited in the detector fell off in a near exponential manner with increasing threshold energy. The data were found to be in reasonable agreement with a computer simulation model developed in our laboratory. The model is used to illustrate how the mass spectra of the residual nuclear fragments shifts towards lower masses with increasing recoil energy. Lighter recoils have longer ranges and a greater chance of leaving a microscopically thin sensitive volume element before coming to their end of range.

79 citations


Journal ArticleDOI
TL;DR: In this article, the amount of charge created by an alpha particle and proton is calculated and the yield of charqes which escape initial recombination is measured, and the experimental results are shown to agree with a charge recombination model where an ionization track radius of 30-40 A is assumed.
Abstract: Highly ionizing heavy charged particles generate significant charge as they pass through the thin thermally grown gate oxide of a MOSFET device. The amount of charge created by an alpha particle and proton is calculated and the yield of charqes which escape initial recombination is measured. The experimental results are shown to agree with a charge recombination model where an ionization track radius of 30-40 A is assumed. Finally, implications of the findings for single charged particle effects in submicron dimension devices are discussed.

77 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of the bias configuration of the source and drain during the irradiation of MOS transistors has been investigated and shown to have a significant effect on the threshold voltage shift measured, as can bias condition applied between the times of irradiation and threshold voltage measurements.
Abstract: It is well known that the bias value applied between the gate and substrate can have a significant effect on the threshold voltage shift of MOS transistors under gamma irradiation. However, not so well known are the facts that the bias configuration of the source and drain during the irradiation also can have a significant effect on the threshold voltage shift measured, as can the bias condition applied between the times of irradiation and threshold voltage measurements. An alternating bias (between "ON" and "OFF" states) applied to the gate during irradiation need not give threshold voltage shifts intermediate between those for the two DC bias conditions. In this paper, we present data demonstrating the importance of these effects and discuss their implications with regards to specifications and techniques for radiation-hardness testing.

75 citations


Journal ArticleDOI
TL;DR: In this paper, the density of radiation-induced trivalent silicon defects at the (111) Si-SiO2 interface was found to be approximately a one-to-one correspondence with radiation induced electronic interface states.
Abstract: Electron spin resonance and capacitance versus voltage measurements demonstrate approximately a one-to-one correspondence between the density of radiation-induced trivalent silicon defects at the (111) Si-SiO2 interface and the density of radiation induced electronic interface states.

Journal ArticleDOI
TL;DR: A 30 period permanent magnet (SmCo5) undulator has been designed, built and tested in this paper, where the period is 6.1 cm, overall length is 1.95 m, and the gap is variable from 2.7 cm to 6.0 cm.
Abstract: A 30 period permanent magnet (SmCo5) undulator has been designed, built and tested. The period is 6.1 cm, overall length is 1.95 m, and the gap is variable from 2.7 cm to 6.0 cm. Magnetic measurements at the midplane with a 2.7 cm gap show that the field is sinusoidal with a peak value of .28 T. Construction details and magnetic measurements are presented along with the spectral distribution of radiation produced by 3.0 GeV electrons traversing the undulator.

Journal ArticleDOI
TL;DR: In this paper, the behavior of optical detectors using microchannel plates (MCPs) as electron multipliers is described in terms of the physical parameters of the MCP (channel resistance, channel capacitance, channel wall secondary emission ratio, etc.).
Abstract: The behavior of optical detectors using microchannel plates (MCPs) as electron multipliers is described in terms of the physical parameters of the MCP (channel resistance, channel capacitance, channel wall secondary emission ratio, etc.). Three operating modes are included: (1) DC operation at low light levels, (2) pulse detection operation at high peak currents, and (3) single electron counting with cascaded V-plate and Z-plate MCPs.

Journal ArticleDOI
TL;DR: In this article, the authors measured flatband voltage shifts in MOS capacitors as a function of incident photon energy and applied electric fields with UV, x-and gamma-ray sources spanning the energy range 70 eV to 1.25 MeV.
Abstract: Radiation-produced flatband voltage shifts in MOS capacitors have been measured as a function of incident photon energy and applied electric fields with UV, x- and gamma-ray sources spanning the energy range 70 eV to 1.25 MeV. Special interest was directed to the energies below 20 keV where the greatest effects on the flatband voltages were expected. At 70 eV the shifts are almost as great as those observed at 1.25 MeV (60Co). For 1.49 keV incident photons the voltage shifts are less than 1/3 those observed for 60Co photons.

Journal ArticleDOI
TL;DR: In this paper, the problem of soft errors in semiconductor devices caused by the protons in the radiation belts is examined, and the authors present a method to estimate the soft error rate in a representative satellite.
Abstract: This paper examines the problem of soft errors in semiconductor devices caused by the protons in the radiation belts. The errors can be produced by a variety of nuclear reactions in silicon. A previous paper presented a calculation of the likelihood of some of these reactions. This information can be combined with knowledge of the proton environment in order to estimate the upset rate for various devices in spacecraft. This paper discusses the proton environment, the effect of spacecraft shielding, the various proton induced reactions in silicon, the calculation of soft error sensitivity, and the soft error rate in a representative satellite.

Journal ArticleDOI
TL;DR: In this paper, a review of beam current and beam quality limits in linear RF and induction accelerators and beam-transport channels is presented, and the role of physical constraints in channel intensity limitation is emphasized.
Abstract: Recent demand for high-intensity beams of various particles has renewed interest in the investigation of beam current and beam quality limits in linear RF and induction accelerators and beam-transport channels. Previous theoretical work is reviewed, and new work on beam matching and stability is outlined. There is a real need for extending the theory to handle the time evolution of beam emittance; some present work toward this goal is described. The role of physical constraints in channel intensity limitation is emphasized. Work on optimizing channel performance, particularly at low particle velocities, has resulted in major technological advances. The opportunities for combining such channels into arrays are discussed.

Journal ArticleDOI
TL;DR: In this paper, the effect of the detection of scattered radiation on the difference image is discussed and it is shown that a conventional scatter reduction grid will improve image quality only if the ratio of the detected scattered photons to the number of detected primary photons is greater than 0.8 when no grid is used.
Abstract: Considerations for the optimum design and use of a computerized fluoroscopy apparatus for performing time dependent image subtraction are presented. The advantages of logarithmic processing are presented. Assuming such processing, the interrelationship of achievable signal to noise, dynamic range and the minimum number of grey levels needed to digitize each image is discussed, and a formula relating these three quantities is derived. Image quality limits imposed by noise sources not associated with the detected x-ray fluence are discussed and a criterion for choosing a maximum x-ray fluence which will not waste patient dose is presented. The limits to spatial resolution achievable with conventional image intensifiers are discussed and it is shown that the maximum one dimensional spatial resolution in the object plane is achieved when the magnification of the x-ray system is such that the image of the x-ray focal spot projected through a point in the object plane onto the detector plane just covers the width of two pixels. The effect of the detection of scattered radiation on the difference image is discussed and it is shown that a conventional scatter reduction grid will improve image quality only if the ratio of the number of detected scattered photons to the number of detected primary photons is greater than 0.8 when no grid is used.

Journal ArticleDOI
K. Unser1
TL;DR: In this article, a beam current monitor using a second harmonic magnetic modulator with an active current transformer in an operational feedback loop was used to obtain wide band response down to dc. The performance of the system depends very much on the magnetic characteristics of the toroidal cores.
Abstract: Beam current is measured with a system combining a second harmonic magnetic modulator with an active current transformer in an operational feedback loop, to obtain wide band response down to dc. A beam current monitor using this principle has been in operation in the CERN Intersecting Storage Rings (ISR) for over 10 years. The original design concept and performance has since been improved. The magnetic modulator-demodulator circuit has two modes of operation: low gain and wide band for initial search until tracking (with the beam current signal) and high gain, narrow band for optimum dc stability during normal operation. A second active L/R integrator loop is added to remove any residual modulator noise from the output signal to improve signal-to-noise ratio in the mid-frequency range. The performance of the system depends very much on the magnetic characteristics of the toroidal cores. The choice of material, measurement methods and core selection is discussed. More recent applications are beam intensity monitors for the CERN Antiproton Accumulator Ring (AA) and the CERN Proton Synchrotron (CPS).

Journal ArticleDOI
TL;DR: In this paper, the authors presented a detailed analysis to predict the galactic cosmic ray induced bit error rate in three commercially availale CMOS RAM types and provided a summary of cyclotron simulation data.
Abstract: The methodology and results are presented for a detailed analysis to predict the galactic cosmic ray induced bit-error rate in three commercially availale CMOS RAM types. A summary of cyclotron simulation data is provided and utilization of the experimental results in the Cosmic Ray Induced Error Rate (CRIER) model is described.

Journal ArticleDOI
TL;DR: In this paper, the authors have shown that a significant improvement in image quality results from such an approach and that coincidence resolving times of less than 500 psec FWHM are easily achievable with cesium fluoride (CsF) detectors.
Abstract: Recent advances in PET designs have shown that a gain in signal-to-noise ratio can be expected by incorporating time-of-flight data in positron emission tomography over the conventional PET mode. It has also been shown that cesium fluoride (CsF) offers the potential of faster timing and high detection efficiency which would be required for a clinical scanner utilizing time-of-flight information. Our research with CsF and the results of a feasibility study of time-off-light positron emission tomography reconstruction have shown that, indeed, a significant improvement in image quality results from such an approach and that coincidence resolving times of less than 500 psec FWHM are easily achievable with CsF detectors. However, the design of fast tomographic systems with multiple detectors which maintain this fast coincidence timing poses a challenging technical problem. The solution to this problem requires a departure from the conventional mode of PET designs to a fast on-line microprocessor based system which is capable of compressing and correcting the data for timing differences, normalization and image function. Such a system is described in this paper and its advantages and disadvantages are discussed.

Journal ArticleDOI
TL;DR: The Multi-Anode Microchannel Arrays (MAMA's) as discussed by the authors are a family of photoelectric photon-counting array detectors being developed for use in instruments on both ground-based and space-borne telescopes.
Abstract: The Multi-Anode Microchannel Arrays (MAMA's) are a family of photoelectric photon-counting array detectors being developed for use in instruments on both ground-based and space-borne telescopes. These detectors combine high sensitivity and photometric stability with a high-resolution imaging capability. Visible-light (10 × 10)-pixel, (1 × 512)-pixel and (1 × 1024)-pixel detector systems are now being used at ground-based telescopes and an ultraviolet (1 × 1024)-pixel detector has been flown in a sounding-rocket spectrometer. A (16 × 1024)-pixel system is currently under test in the laboratory and (24 × 1024)-pixel and (256 × 1024)-pixel systems will be available later this year. The construction and modes-of-operation of the different detector systems are described and the latest performance data are presented.

Journal ArticleDOI
TL;DR: In this paper, a gallium arsenide photocathode is illuminated by the optical beam from a frequency doubled, actively mode-locked and Q-switched Nd:YAG laser.
Abstract: For the generation of intense single and multiple bunches of electrons (>8 nc per bunch) for accelerator studies at SLAC, a high peak current photoemission electron gun has been developed. A gallium arsenide photocathode is illuminated by the optical beam from a frequency doubled, actively mode-locked and Q-switched Nd:YAG laser. The mode-locked optical pulses are of variable, sub-nanosecond width and occur with a spacing of 8.4 nsec, synchronized with the 2856 MHz accelerator rf. The gun is designed to be space charge limited at 15 A and 200 kV, although emission of 60 A was obtained with a 57 kV test structure, corresponding to a current density of 180 A/cm2. With the proper choice of laser wavelength, the electron beam may be 40% longitudinally polarized.

Journal ArticleDOI
TL;DR: In this paper, a Monte-Carlo computer code was developed that tracks the Compton and photoelectric interactions of photons incident on a linear array of detectors, until the photon is tracked until it either escapes the array or is photoelectrically absorbed in a detector or septum.
Abstract: In positron emission tomographs employing arrays of detectors, the useful detection efficiency and spatial resolution depend on the size and type of detectors, the septa between the detectors, the angle of incidence, and the extent to which the pulse height selection rejects multiple detector interactions To determine the relative effect of these factors a Monte-Carlo computer code was developed that tracks the Compton and photoelectric interactions of photons incident on a linear array of detectors The photon is tracked until it either escapes the array or is photoelectrically absorbed in a detector or septum A photon is successfully detected whenever the energy-loss threshold is exceeded in only one detector Results are tabulated for bismuth germanate (BGO), NaI(Tl), CsF, germanium, plastic and lead loaded plastic detectors from 01 cm X 1 cm X 1 cm to 5 cm X 10 cm X 10 cm; for lead septa between detectors; for energy loss thresholds from 0 to 511 keV; and for angles of incidence from 0 to 30 degrees We show that for a given detector size, BGO has the best efficiency and that this advantage is most pronounced for narrow detectors

Journal ArticleDOI
TL;DR: In this article, a new sampling scheme applicable to the circular ring geometry positron camera is described, which employs Dichotomic-Ring (two half rings) with linear motion which allows parallel or fan mode sampling with any desired degree of sampling interval.
Abstract: A new sampling scheme applicable to the circular ring geometry positron camera is described. The new scheme employs Dichotomic-Ring (two half rings) with linearmotion which allows parallel or fan mode sampling with any desired degree of sampling interval. The parallel and fan data sets obtained by dichotomic motion provide d/4 and d/2 samplings where d is the detector to detector spacing. Computer simulations were made which confirmed the expected performances and results are compared with other conventional schemes such as wobbling and d/2 angular motion sampling schemes for a ring geometry positron camera.

Journal ArticleDOI
TL;DR: In this article, the short and long-term anneal of radiation-induced flatband voltage shift in both Al and Si-gate MOS capacitors following pulsed e-beam irradiation is examined.
Abstract: The short- and long-term anneal of radiation-induced flatband voltage shift in both Al- and Si-gate MOS capacitors following pulsed e-beam irradiation is examined. The short-term anneal was measured and found to be similar for both Al- and Si-gate capacitors. Experiments were performed to investigate the dependence of the long-term anneal on oxide thickness, temperature, and bias. The Al-gate capacitors exhibited a low interface-state buildup following irradiation and had a long-term annealing curve with a simple ln(t) dependence, while the Sigate capacitors studied had a more complicated annealing curve due to the buildup of a larger number of interface states and lateral nonuniformities (LNUs). Thinning the gate oxide was found to dramatically reduce the effects of interface states and LNUs on the long-term anneal. In capacitors where the effects of interface states and LNUs are small the long term annealing was found to be only weakly temperature dependent over the range -60 to 100°C, and removal of bias following irradiation had little effect. On the other hand, the long-term annealing of capacitors with a significant buildup of radiation-induced interface states and LNUs exhibited a strong temperature and post-radiation bias dependence. Some implications of the experimental results for the proper design of test procedures for determining radiation susceptibility are discussed.

Journal ArticleDOI
TL;DR: In this article, the beam losses caused by charge-changing collisions between heavy ions and residual gas molecules in a synchrotron have been calculated for different injection energies and ionic charge states.
Abstract: Experimental charge-changing cross sections for uranium ions incident on H2 and N2 at 1.4 MeV/u are presented and extrapolation to higher energies is discussed briefly. The beam losses caused by charge-changing collisions between heaviest ions and residual gas molecules in a synchrotron have been calculated for different injection energies and ionic charge states. For example, if a beam of U+10-ions is accelerated from 1.4 MeV/u to 100 MeV/u by an average electric field BR=112 V/m an average working pressure of about 1×10-11 mbar is necessary to limit beam losses to several percent.

Journal ArticleDOI
TL;DR: In this article, the characteristics and performance of several kinds of high-gain micro-channel plate photomultipliers have been investigated, focusing on lifetime studies, performance in the magnetic field, and timing properties.
Abstract: The characteristics and performance of several kinds of high-gain micro-channel plate photomultipliers have been investigated. Special attention was directed towards i) lifetime studies, ii) performance in the magnetic field, and iii) timing properties. Lifetime studies include separate investigations of the photocathode quentum efficiency degradation caused by ion feedback, and the deterioration of the micro-channel plate gain. The dependence of the micro-channel plate photomultiplier gain on the intensity and the direction of the magnetic field (up to 7 kGauss) is reported.

Journal ArticleDOI
TL;DR: In this paper, a new system (NEUROECAT) was designed and built for quantitative positron emission computed tomography (PCT) of the brain, which consists of three octagonal arrays of bismuth germanate detectors providing 5 simultaneous image planes.
Abstract: A new system (NEUROECAT) has been designed and built for quantitative positron emission computed tomography (PCT) of the brain. It consists of three octagonal arrays of bismuth germanate detectors (BGO) providing 5 simultaneous image planes. The design utilizes unique shielding and detector geometries which optimize uniformity in image and axial resolution and also minimize scatter and accidental coincidence rates. The basic system image resolution is 11.0±.4 mm FWHM with a total system sensitivity of 270,000 counts/sec/microcurie/cc uniformly dispersed in a 20 cm diameter cylinder.

Journal ArticleDOI
Ingo Hofmann1
TL;DR: In this paper, the authors compared analytic work and computer simulation results and showed that the nonlinearity required for coupling is caused by instability, which grows out of arbitrarily small initial fluctuations, and special emphasis was given to the coupling instability in case of considerably different energy content in two phase planes.
Abstract: In linear devices the effective phase space volume occupied by a beam can grow rapidly if the beam intensity is sufficiently close to the space charge limit and if a source of instability is available, like a periodic variation of the focusing force and/or considerable anisotropy between different phase planes. Results from analytic work and computer simulation are compared and shown to support each other. Regimes are defined in terms of tunes and tune depressions, where no emittance growth should occur; special emphasis is given to the coupling instability in case of considerably different energy content in two phase planes. The amount of transfer is found to depend critically on the strength of tune depression. The nonlinearity required for coupling is shown to arise from instability, which grows out of arbitrarily small initial fluctuations.