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In the past few years, there has been a growing interest for direct-field electron acceleration with ultra-intense and ultrafast radially polarized laser beams. This particular acceleration scheme offers the possibility of producing highly collimated mono-energetic relativistic attosecond electron pulses from an initial cloud of free electrons that could be produced by ionizing a nanoparticle. In this paper, we describe how electron energy scales with laser power and we explain how the beam waist size and the pulse duration can be optimized for maximal acceleration. The main conclusion of our work is that an electron can effectively reach the high-intensity optical cycles of this particular beam and be optimally accelerated without the necessity of being released by photoionization near the pulse peak.

To lower the trapping threshold and partially overcome the dephasing problem, a certain axial plasma density profile is desired. To obtain such a density distribution, a laser heating method is proposed and numerically tested in this paper. By using this method, a density downramp and then upramp can be formed. When a laser wake wave passes through such a downramp density, plasma electrons are trapped into the acceleration phase. Propagating in an upramp density, the energy of the trapped electrons would be considerably enhanced.

Rapid developments in the area of micro-sensors for various applications such as structural health monitoring, bio-chemical sensors and pressure sensors have increased the demand for portable, low cost, high efficiency energy harvesting devices. In this paper, we describe the scheme for powering a pulse rate sensor with a vibration energy harvester integrated inside a pen commonly carried by humans in the pocket close to the heart. Electromagnetic energy harvesting was selected in order to achieve high power at lower frequencies. The prototype pen harvester was found to generate 3 mW at 5 Hz and 1 mW at 3.5 Hz operating under displacement amplitude of 16 mm (corresponding to an acceleration of approximately 1.14 grms at 5 Hz and 0.56 grms at 3.5 Hz, respectively). A comprehensive mathematical modelling and simulations were performed in order to optimize the performance of the vibration energy harvester. The integrated pen harvester prototype was found to generate continuous power of 0.46–0.66 mW under normal human actions such as jogging and jumping which is enough for a small scale pulse rate sensor.

The results of a theoretical consideration of positron acceleration in the plasma wakefield driven by asymmetric laser pulses are presented in this paper. It is found that the asymmetric laser pulse can significantly modify the phase portrait of the positron dynamics and enhance the maximum energy of the accelerated positrons. There exists an optimum ratio of the lengths of the rising and falling segments of the asymmetric laser pulse. There exists also an upper limit on plasma density to get the maximum wakefield potential.

Aside from LISA Pathfinder's top-level acceleration requirement, there is a stringent independent requirement for the accuracy of the optical metrology system. In case of a perfectly aligned metrology system (optical bench and test masses) it should rather be independent of residual displacement jitter due to control. However, this ideal case will not be achieved as mechanical tolerances and uncertainties lead to a direct impact of test mass and spacecraft displacement jitter on the optical measurement accuracy. In this paper, we present a strategy how to cover these effects for a systematic requirement breakdown. We use a simplified nonlinear geometrical model for the differential distance measurement of the test masses which is linearized and linked to the equations of motion for both the spacecraft and the two test masses. This leads from test mass relative displacement to a formulation in terms of applied force/torque and thus allows to distinguish the absolute motion of each of the three bodies. It further shows how motions in each degree of freedom couple linearly into the optical measurement via DC misalignments of the laser beam and the test masses. This finally allows for deriving requirements on the alignment accuracy of components and on permittable closed-loop acceleration noise. In the last part a budget for the expected measurement performance is compiled from simulations as no measurement data is available yet.

The test masses of LISA Pathfinder are free flying and therefore not grounded to the spacecraft by a wire. Because of galactic cosmic rays, solar energetic particles, and unknown microscopic surface effects during initial test mass release, an unacceptable level of absolute charge might be present on the test masses. A charged test mass can endanger transition to high accuracy control modes which are required for science experiments. Furthermore, charged test masses introduce unwanted disturbance accelerations for example due to Coulomb interactions with surrounding conducting surfaces. The charge management system is designed to discharge the test masses up to a tolerable level of absolute charge such that the mission goal can be achieved. It is therefore an essential part of the experiments to be performed with the LISA Technology Package. The paper describes charge management tasks to be performed on board the spacecraft and summarizes the principles of charge measurement and discharge control. An overview of the experiment operations is given where the interconnection of operational charge management system modes and operational modes of the drag-free, suspension and attitude control system is considered. Simulated performance results are presented.

The movement of bubble is a basic subject in gas-liquid two-phase flow research. A method for calculating bubble volume which is one of the most important characters in bubble motion research was proposed. A suit of visualized experimental device was designed and set up. Single bubble rising in stagnant liquid in a rectangular tank was studied using the high-speed video system. Bubbles generated by four orifice with different diameter (1mm, 2mm, 3mm, 4mm) were recorded respectively. Sequences of recorded high-speed images were processed by digital image processing method, such as image noise remove, binary image transform, bubble filling, and so on. then, Several parameters could be obtained from the processed image. Bubble area, equivalent diameter, bubble velocity, bubble acceleration are all indispensable in bubble volume calculating. In order to get the force balance equation, forces that work on bubble along vertical direction, including drag force, virtual mass force, buoyancy, gravity and liquid thrust, were analyzed. Finally, the bubble volume formula could be derived from the force balance equation and bubble parameters. Examples were given to shown the computing process and results. Comparison of the bubble volume calculated by geomettic method and the present method have shown the superiority of the proposed method in this paper.

In this paper, the effects of scale length and transition density ratio on the electron trapping and acceleration with a sharp density transition in laser wakefield accelerator (LWFA) have been studied using one-dimensional particle-in-cell (PIC) simulations. Simulation results show that the number of accelerated electrons depends on the plasma density in the high density region and the scale length of the density transition region. For the detailed investigation of the dynamical features of the electron trapping and acceleration, spatiotemporal patterns of the laser wake wave are also used. Throughout this work, the optimum condition for the electron acceleration could be found in the relevant parameter space of the scale length and the transition density ratio.

Atom interferometers have been shown to be very stable and accurate sensors for acceleration and rotation. In this paper we review the applications of atom interferometry to gravity measurements, with a special emphasis on the potential impact of these techniques on applied science fields.

For more than a decade, the study of microturbulence driven by ion temperature gradient (ITG) drift instabilities in tokamak devices has been an active area of research in magnetic fusion science for both experimentalists and theorists alike. An important impetus for this avenue of research was the discovery of the radial streamers associated with the ITG modes in the early 1990s using the particle-in-cell (PIC) simulation method. Subsequently, ITG simulations using codes with increasing realism have been made possible by the dramatic increase in computing power. Notable examples were the demonstration of the importance of nonlinearly generated zonal flows in regulating ion thermal transport and the transition from Bohm to gyroBohm scaling with increased device size. In this paper, we will describe an interesting nonlinear physical process, as well as the resulting turbulent transport, that is associated with the interactions between the nonlinear parallel acceleration of the ions and the zonal flow modes. This study was carried out by utilizing a fully parallelized three-dimensional PIC code in global toroidal geometry on the most advanced, modern, massively parallel supercomputers.

Study of fluid instabilities such as Rayleigh?Taylor and Richtmyer?Meshkov instabilities requires accurate computational modeling of dynamically moving fronts. This paper reports the verification and validation of the FronTier code and its applications to the fluid mixing problem. We show that the Lagrangian front tracking method provides high resolution to the front and the tracked solution gives significant enhancement of buoyancy acceleration in Rayleigh?Taylor instability and enstrophy generation in the shock-driven Richtmyer?Meshkov instability.

This paper reports the development and implementation of an energy aware autonomous wireless condition monitoring sensor system (ACMS) powered by ambient vibrations. An electromagnetic (EM) generator has been designed to harvest sufficient energy to power a radio-frequency (RF) linked accelerometer-based sensor system. The ACMS is energy aware and will adjust the measurement/transmit duty cycle according to the available energy; this is typically every 3 s at 0.6 m s?2 rms acceleration and can be as low as 0.2 m s?2 rms with a duty cycle around 12 min. The EM generator has a volume of only 150 mm3 producing an average power of 58 ?W at 0.6m s?2 rms acceleration at a frequency of 52 Hz. In addition, a voltage multiplier circuit is shown to increase the electrical damping compared to a purely resistive load; this allows for an average power of 120 ?W to be generated at 1.7 m s?2 rms acceleration. The ACMS has been successfully demonstrated on an industrial air compressor and an office air conditioning unit, continuously monitoring vibration levels and thereby simulating a typical condition monitoring application

This paper presents a design and optimization strategy for resonant electromagnetic vibration energy harvesting devices. An analytic expression for the magnetic field of cylindrical permanent magnets is used to build up an electromagnetic subsystem model. This subsystem is used to find the optimal resting position of the oscillating mass and to optimize the geometrical parameters (shape and size) of the magnet and coil. The objective function to be investigated is thereby the maximum voltage output of the transducer. An additional mechanical subsystem model based on well-known equations describing the dynamics of spring–mass–damper systems is established to simulate both nonlinear spring characteristics and the effect of internal limit stops. The mechanical subsystem enables the identification of optimal spring characteristics for realistic operation conditions such as stochastic vibrations. With the overall transducer model, a combination of both subsystems connected to a simple electrical circuit, a virtual operation of the optimized vibration transducer excited by a measured random acceleration profile can be performed. It is shown that the optimization approach results in an appreciable increase of the converter performance.

Dynamic magnetic resonance imaging (MRI) is a challenging problem because the MR data acquisition is often not fast enough to meet the combined spatial and temporal Nyquist sampling rate requirements. Current approaches to this problem include hardware-based acceleration of the acquisition, and model-based image reconstruction techniques. In this paper we propose an alternative approach, called PARADIGM, which adapts both the acquisition and reconstruction to the spatio-temporal characteristics of the imaged object. The approach is based on time-sequential sampling theory, addressing the problem of acquiring a spatio-temporal signal under the constraint that only a limited amount of data can be acquired at a time instant. PARADIGM identifies a model class for the particular imaged object using a scout MR scan or auxiliary data. This object-adapted model is then used to optimize MR data acquisition, such that the imaging constraints are met, acquisition speed requirements are minimized, essentially perfect reconstruction of any object in the model class is guaranteed, and the inverse problem of reconstructing the dynamic object has a condition number of one. We describe spatio-temporal object models for various dynamic imaging applications including cardiac imaging. We present the theory underlying PARADIGM and analyze its performance theoretically and numerically. We also propose a practical MR imaging scheme for 2D dynamic cardiac imaging based on the theory. For this application, PARADIGM is predicted to provide a 10?25 ? acceleration compared to the optimal non-adaptive scheme. Finally we present generalized optimality criteria and extend the scheme to dynamic imaging with three spatial dimensions.

Researchers studying aspects of locomotion or movement in biological and biomimetic systems commonly use video or stereo video recordings to quantify the behaviour of the system in question, often with an emphasis on measures of position, velocity and acceleration. However, despite the apparent simplicity of video analysis, it can require substantial investment of time and effort, even when performed with adequate software tools. This paper reviews the underlying principles of video and stereo video analysis as well as its automation and is accompanied by fully functional and freely available software implementation.

This paper discusses the feasibility of electrostatic space propulsion which uses microparticles as propellant. It is shown that particle charging in a plasma is not sufficient for electrostatic acceleration. Moreover, it appears technically difficult to extract charged particles out of a plasma for subsequent acceleration without them being discharged. Two novel thruster concepts are proposed. In the first one, particles with low secondary electron emission are charged using energetic electrons in the order of magnitude of 100eV. The second concept charges the particles by contact with needle electrodes at high electrostatic potential ( 20kV). Both methods allow the maximum possible charges on microparticles.

A heuristic semi-classical kinetic theory of turbulence in magnetized plasmas was formulated in the 1960s, but the statistical mechanical formulation of the same problem, which is necessary for a quantitative analysis, has not been accomplished. Recently, the present authors formulated the statistical mechanical kinetic turbulence theory in a formal manner (P H Yoon 2007 Phys. Plasmas 14 10230, P H Yoon and T-M Fang 2007 Phys. Plasmas 14 102303). In this paper, the parallel cascade of Alfven waves via the three-wave decay process is numerically investigated on the basis of the results outlined in the above references. It is shown that the cascade of low-frequency Alfven waves to high-frequency ion-cyclotron and magnetosonic waves takes place mediated by ion-sound turbulence. The Alfven wave cascade is important, for instance, in the solar wind acceleration and coronal heating problem, since the low-frequency, long-wavelength Alfven waves must first undergo cascade to high-frequency, short-wavelength modes in order for cyclotron resonant absorption to take place. The cyclotron resonance is believed to be important for charged-particle acceleration in the aforementioned applications. The present analysis may be important in such a context.

This paper presents a new solution to the on-line continuous measurement of particle size and particle velocity within a dilute gas/solid pneumatic pipeline, using low-cost optoelectronic components and imaging hardware. A low-cost, single CCD colour digital camera is used with high power light emitting diodes (LEDs) of different wavelengths, which are driven with very narrow pulses during each camera frame. These resulting frames consist of multiple images of the same particle at different instances in time, by correlating these images it is possible to calculate the size and velocity for each individual particle to high accuracy as the blur due to the finite exposure time can be calculated and removed. As multiple images are taken of the same particle it is possible to extrapolate other information, including acceleration, rotation and direction of movement. The results from this research are very promising and the technique may provide a satisfactory solution to the long standing industrial measurement problem. This system is specifically developed for the measurement of particle sizes in the range of 10?m to 1,000?m, but the technique can be applied equally well to particles outside these limits.

Over-loading is a common problem in some developing countries. Currently, large and fixed measurement systems are used to measure the load of vehicles travelling on highways. This paper presents an on-vehicle measuring device, which is based on measurement of change in capacitance due to variation in distance between electrodes mounted on vehicles. The on-vehicle leaf springs are used as a key part of the weighing transducer. Acceleration transducers are used to measure the vehicle's forward and the vertical accelerations. A feature of this on-vehicle measuring device is that it can provide both static and dynamic load measurements. The drivers can check the load in the cab, and the highway inspectors can check the load at any time and any place through radio communication, thus identifying over-loaded vehicles.

In this paper, the characteristics of the acceleration sensor utilizing the resonance frequency change in the flexural vibrator are examined experimentally. The sensor sample was produced using stainless steel. It was confirmed that the relationship between the applied acceleration and the resonance frequency change becomes linear and almost coincides with the theoretical value by the finite element analysis. The sensor sensitivities of approximately 2800 ppm/G and 2150 ppm/G are measured in the cases of using the 1st and 2nd modes, respectively. It was clarified experimentally that the spurious vibrations do not appear in the vicinity of the resonance frequency f 0. Moreover, it is shown that this sensor can also be used as an inclination angle sensor.

This paper describes the development process for acceleration sensors used on automobiles and an acceleration evaluation system designed specifically for acceleration at super-low-range frequencies. The features of the newly developed sensor are as follows. 1) Original piezo-bimorph design based on a disc-center-fixed structure achieves pyroeffect cancelling and stabilization of sensor characteristics and enables the detection of the acceleration of 0.0009 G at the super-low-range-frequency of 0.03 Hz. 2) The addition of a self-diagnostic function utilizing the characteristics of piezoceramics enables constant monitoring of sensor failure. The frequency range of acceleration for accurate vehicle motion control is considered to be from DC to about 50 Hz. However, the measurement of acceleration in the super-low-range frequency near DC has been difficult because of mechanical and electrical noise interruption. This has delayed the development of the acceleration sensor for automotive use. We have succeeded in the development of an acceleration evaluation system for super-low-range frequencies from 0.015 Hz to 2 Hz with detection of the acceleration range from 0.0002 G (0.2 gal) to 1 G, as well as the development of a piezoelectric-type acceleration sensor for automotive use.

Cell projection electron beam lithography has been developed to achieve high throughput, and this system is now available commercially. However, the cell projection method uses a beam current that is much higher than that of the variable shaped beam method, and the Coulomb interaction caused by electrical repulsion (the coulomb effect) is thus much stronger. It is important to control the Coulomb effect in fine pattern fabrication because it causes beam blur that degrades resolution. This paper describes the effects of the acceleration voltage on the resolution of fine patterns below 100 nm as determined through experiments and simulations. Using an electron beam (EB) lithography system with 70 kV acceleration, we made 120 nm pitch lines and spaces (L&S) patterns by the cell projection method. Throughput was improved by using an acceleration voltage higher than the usual 50 kV acceleration. Because the Coulomb effect under 70 kV acceleration is weaker, we could use a higher beam current density or a larger cell projection size. The 70 kV acceleration is particularly useful for fine patterns and enables throughput twice that possible with 50 kV acceleration for 70 nm L&S pattern delineation.

The long-period (~600 yr) binary system 36 Ophiuchi AB consists of two chromospherically active K dwarfs. If we constrain the period using the mass-luminosity relation and the observed parallax, the remaining orbit parameters can be estimated from the 170 years of visual-binary observations. In this paper, we further constrain the orbit by precise measurements of the differential radial velocities (with arbitrary zero points) of both 36 Oph A and B and the difference in radial velocity between 36 Oph B and A. Our best orbit gives a good fit to the visual-binary observations, the difference in velocity, and the mean radial acceleration of A; but the observed acceleration of B is a factor of 164 larger than the value predicted by the orbit. This factor is so large that no reasonable variation in the adopted sum of masses, mass ratio, parallax, or orbit parameters will remove the B acceleration discrepancy. Ths maximum companion mass allowed by the residuals from the visual-binary orbit is of order 8 Jupiter masses for assumed periods between 30 and 100 years so the 36 Oph B acceleration discrepancy would ordinarily make it a candidate for a substellar companion. However, the very high eccentricity (~0.9) of the binary-star orbit means its closest approach is of order 6 a.u. making it unlikely that any substellar companions would form or survive with the semi-major axis exceeding ~1.5 a.u. or period exceeding ~2 years. Thus, 36 Oph B is an important counter-example which serves as a warning that for chromospherically active stars, at least, it is possible to have apparent radial accelerations in the absence of substellar companions.

This paper describes a precise method of determining the supporting position of a stress compensated (SC) cut crystal wafer using a semiconductor pulsed laser. Because the supporting position greatly influences the frequency stability against acceleration and/or external stress, an accurate determination method is required. The experimental results for circular SC-cut quartz resonators with various supporting positions demonstrate the validity of this technique.

A new electron acceleration mechanism of the inverse synchrotron radiation which was proposed in a paper (Jpn. J. Appl. Phys. 28 (1989) L704) is reexamined in order to show that an electron can be accelerated well by a realistic Gaussian-pulse electromagnetic wave. Numerical analyses and particle simulations were performed in addition to the simple analyses which present the scaling law for the acceleration energy and the expression for the optimal applied weak static magnetic field of this system.

The paper studies the distribution function of a runaway electron beam with allowance for close collisions of fast tail electrons with thermal ones, as a result of which momentum is imparted to the latter sufficient for escape into a continuous acceleration regime. It is shown that a beam is formed which is not in equilibrium with respect to transverse momenta; it may excite electromagnetic plasma instabilities under the conditions of linear and non-linear electron cyclotron resonance.

A promising physical process able to provide efficient particle acceleration in a plasma is the surfatron. In the basic picture a particle is accelerated without limit when it is trapped by a potential wave moving perpendicularly to a uniform magnetostatic field. In this paper we study surfatron acceleration due to a wave packet with waves evenly spaced in phase speed. Particles are accelerated by two mechanisms: diffusive acceleration due to the local instability leading to chaos and coherent acceleration due to trapping in the available subluminal waves. The probability of trapping in each wave is derived analytically and confirmed numerically. We account for the perturbations due to the other waves of the packet and find the arising of intermittency between chaos and regular motion. The consequences of this phenomenon are discussed.

In this paper, four different LDA system configurations are compared with respect to their application to time-periodic flows. The four configurations are: (i) a phase-locked loop analog tracker followed by a multichannel analyzer which give the distribution of velocity and acceleration, (ii) a digital correlator that produces the photon correlation function which yields the velocity distribution as well, (iii) an Erdmann/Gellert type one beam rate correlation setup that measures velocity correlations, and (iv) an extended rate correlation setup using cross beam geometry and Bragg shift frequency offset for the selection of single velocity components. The comparison includes measurement time, computational effort and the applicability to special flow situations. As a test flow we used the well known Taylor vortices, which show various flow patterns depending on the Reynolds number, especially a region where the velocity varies periodically.

The Polytron is a toroidal plasma configuration, using 36 magnetic cusps joined point-to-point. This paper presents observations of the acceleration and containment of the plasma. Measurement of the force on the plasma shows that the initial acceleration is given by a particle equation mi(dvphi /dt)=ZeEphi and occurs in thin sheaths in the ring cusp planes. The concept of a non-magnetic effective inductance is experimentally verified. However rapid, although not complete loss of plasma occurs after 1 mu sec for argon, limiting the electron temperature to 30 eV at an electron density of 1020 m-3. This loss is expected and an energy balance at this time implies that electron thermal conduction causes the principal loss of energy. After this loss, the rest of the plasma drifts to the outer wall of the vacuum vessel after about 3 mu sec.

The instrument was developed for the measurement of the acceleration of the rear axle of a vehicle. It was necessary for the recording to be done remotely in order accurately to phase three records, two of acceleration and one of spring load. A new method of remote recording has been developed for the purpose. The paper describes the design of the instrument, its principle of operation, and also, though briefly, the auxiliary equipment. The undamped natural frequency is 300 similar and the maximum reading is 25 g. Damping is provided by filling the casing with light mineral oil and, although less than critical, is sufficient to eliminate from the records any disturbance due to self-oscillation.

In this paper the phenomena of total reflexion are considered, de novo, from the standpoint of the Principle of Huygens, no use whatever being made of the Fresnel formulae for reflexion and refraction. Huygens' principle enables us to evaluate the disturbance appearing in the second medium when light is incident on the boundary between two media and is totally reflected into the first medium. The disturbance takes the form of a superficial wave moving parallel to the boundary. The existence of such a superficial wave is then shown to involve, as a necessary consequence, an acceleration of the reflected wave with reference to the incident wave, the acceleration being zero at critical incidence and increasing to half an oscillation at grazing incidence. The intensity of the superficial wave is at critical incidence greater for the component having the magnetic vector parallel to the surface, but diminishes more rapidly with increasing incidence than for the component having the electric vector parallel to the surface; the phase-advance reaches its maximum value correspondingly sooner. The phase-angle between the two components is evaluated and found to be an acute angle, in agreement with the classical treatment based on the Fresnel formulae, but in disagreement with the conclusions of Lord Kelvin and Schuster. The source of error in the Kelvin-Schuster treatment is pointed out. Experimental evidence regarding the magnitude of the phase-advance of each component separately is available and is in agreement with the classical theory. Finally, a method is described by which the distribution of intensity, state of polarisation, and direction of flow of energy in the superficial wave may be studied experimentally.

More experimental information about the nature of the binding forces between nuclear constituents is necessary before an advance in fundamental nuclear physics can be achieved. By considering the type of information which would be most useful, the conclusion is reached that it necessary to have available protons of energies of about 1000 MeV. in order to carry out the necessary experiments. It is with a method of obtaining protons of this energy that this paper is concerned. An examination of the possibilities of achieving such high energy protons by the existing methods leads to a pessimistic conclusion, and a new method is suggested. This new method, the synchrotron, is described in principle, and its advantages are outlined, a very important factor being its comparatively low cost. An accelerator of this type is being built at Birmingham University with a grant from the Department of Scientific and Industrial Research, and its design is considered in some detail. The magnet and its excitation form the greatest part of the apparatus in size and cost. Several alternative methods are suggested and discussed for both the magnet design and its method of excitation. An air-cored magnet is considered but rejected because of the very large mechanical forces involved and the precision required in positioning the conductors. As a result an iron-cored magnet has been chosen for construction. The excitation of the magnet is to be achieved by a d.c. motor-generator supplied with a fly-wheel. The requirements of the accelerating system, in which is included a radio frequency which changes by a ratio of about 1: 36 during the acceleration, are quite exacting. The methods by which it is hoped that these requirements will be met are outlined. The problems associated with injection and extraction of the particles receive some attention, and a schematic description of the proposed vacuum chamber is included. When protons of energies greater than 1010 eV. are to be obtained by a synchrotron, the cost of the device becomes overwhelming and some alternative method will have to be suggested. The application of the synchrotron being built at Birmingham to accelerating electrons, is limited to achieving electron energies of about 300- 00 MeV. because of radiation losses.

Using a CV76 magnetron at a wave-length of 10.0 cm. (maximum power 500 kw.; power available for acceleration, 300 kw.), and a 3-stage single cavity, electrons were accelerated to a voltage of 0.85 Mev. The expected figure was approximately 1.1 Mev. The paper describes the R.F. work involved in obtaining the result.

In the ‘polytron’ a series of cusp magnetic fields is superimposed on a toroidal discharge. Stability is improved by favourable field curvature, and containment will be good if the plasma acquires a substantial velocity relative to the cusps. This can be achieved by a Hall acceleration mechanism. In this paper a hydromagnetic analysis is presented in which realistic time variations of electric and magnetic fields are allowed, and plasma self-fields are included. An upper bound is set to the acceleration obtainable from a given cusp system and expressed as a critical electric field Ec. The existence of Ec is confirmed experimentally, and it is possible to reproduce experimental waveforms approximately by inserting appropriate parameters into the equations. The effect of a toroidal magnetic field is also considered and a criterion derived for its maximum permissible value. In designing a fusion device this criterion could be an important consideration.

When working out the theory of high frequency beam stacking in accelerators operating with a constant magnetic field it is important to take into account the perturbations of the beam which has already been stacked caused by later acceleration cycles. The main effect of these perturbations is to increase the energy spread of the beam and to alter its mean energy. This paper presents a general formulation of this problem and a solution is given for certain particular cases.

This paper describes the neutron emission observed during an investigation of the characteristics of fast linear Z-pinches using a low-inductance condenser bank. The neutron production is compared with the results obtained elsewhere and is shown to be different in several respects from that obtained with low-power banks, but is quite similar to that reported in more recent, high-power experiments. It is shown that much of the yield is non-thermonuclear, and a number of existing theories for the production of neutrons by acceleration processes in a plasma are discussed. A process of neutron production in fast linear pinches is suggested, which qualitatively accounts for many recently reported results; the proposed mechanism becomes the well-known Colgate process in discharges where m = 0 instabilities lead to narrow necks in the plasma. Reasons are given to account for the absence of appreciable thermonuclear yields which might be expected from theoretical considerations.

This paper gives a short description of some of the properties of accelerators having a vertically increasing field. A discussion is given of the requirements which must be met for optimum acceleration, as well as questions dealing with the existence of equilibrium orbits, the stability of betatron oscillations and the particle acceleration process in accelerators of this type.

The design of a chronograph which will give a time trace subdivided into units and fractional units requires the association of a rotating system and a vibrating or time-keeping system. It a low-frequency vibrating system be employed, the rotating system, although keeping good average time, may show exaggerated errors in unit subdivisions due to acceleration and deceleration between periods of control. The Paper discusses the association of a high-frequency synchronous alternating-current motor with a high-frequency valve-maintained tuning-fork. It deals with the design of valve-maintained motors and condenser-tuned valve-maintained tuning-forks and gives expressions for the frequency of the maintained system for motors coupled to tuning-forks both without and with tuning condensers.

Attention is drawn to an error in the paper of Champeney and Moon. The simplest interpretation of this experiment and that of Moon et al. is that time dilatation is a consequence of acceleration and not of relative velocity.

The paper describes a simple apparatus by means of which the acceleration of gravity can be easily demonstrated. Distances travelled by a falling body during successive time units can be projected directly on to a screen. The apparatus is essentially an arrangement for projecting light from a falling drop of water, the light being interrupted at a constant frequency by revolving sectors.

This paper describes measurements of the ablation pressure for 10.6 µm and 1.05 µm laser irradiation using thin-foil acceleration observed by X-ray backlighting and X-ray streak shadow graphs of the implosion of a spherical target. At an absorbed laser intensity of 1014 W/cm2, the ablation pressure was more than 10 Mbar for laser wavelengths of 10.6 µm and 1.05 µm. The results are compared with theories based on the self-regulated flow model and the flux-limited thermal conduction model.