... the source of high-energy emission. ... Categories : OPTICS PARTICLE ACCELERATORS NUCLEAR PHYSICS & ELEMENTARY ...
DTIC Science & Technology
From the non detection of X-ray signatures upper limits of the number and energy content of shock-accelerated electrons are inferred. ...
NASA Website
We review basic constraints on the acceleration of ultra-high-energy (UHE) cosmic rays (CRs) in astrophysical sources, namely, the geometric (Hillas) criterion and the restrictions from radiation losses in different acceleration regimes. Using the latest available astrophysical data, we redraw the Hillas plot and ...
NASA Astrophysics Data System (ADS)
Inertial fusion target physics imposes important constraints on the design of linacs for heavy-ion fusion. The most challenging constraint from a scientific standpoint is the requirement that the accelerator deliver more than 10{sup 14} W of beam power to a small quantity (less than 100 mg) of matter. The most challenging ...
Energy Citations Database
In this paper, the authors describe modifications to MAD version 8.23 to include linear accelerator cavities and beam acceleration. An additional energy variable has been added which is modified as the beam passes through LCAV elements (linear accelerator cavities) and can be used as a ...
DOE Information Bridge
Staging laser plasma accelerators is an efficient way of mitigating laser pump depletion in laser driven accelerators and necessary for reaching high energies with compact laser systems. The concept of staging includes coupling of additional laser energy and transporting the electron beam from one ...
Large fusion devices will almost certainly produce net energy. However, a successful commercial fusion energy system must also satisfy important engineering and economic constraints. Inertial confinement fusion power plants driven by multi-stage, heavy-io...
National Technical Information Service (NTIS)
We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time ...
Recent successes in laser-ion acceleration have motivated research towards laser-driven compact accelerators for medical therapy. Realizing laser-ion acceleration for medical therapy will require adapting both the laser-ion acceleration to the medical requirements, as well as the treatment methodology to the ...
Siberian Snakes provide a practical means of obtaining polarized proton beams in large accelerators. The effect of snakes can be understood by studying the dynamics of spin precession in an accelerator with snakes and a single spin resonance. This leads to a new class of energy independent spin depolarizing resonances, called snake ...
We discuss accelerator production of neutrinos in underground laboratories via the 12C(p, n)12N reaction. Proton beams within the reach of current accelerator design and economic constraints can produce fluxes up to ten times that attributed to the sun. Intense neutrino fluxes in low-background environments would open up new ...
Cosmic rays are ubiquitous in space, and are apparently present wherever the matter density is small enough that they are not removed by collisions with ambient particles. The essential similarity of their energy spectra in many different regions places significant general constraints on the mechanisms for their acceleration and ...
It is anticipated that radiation heating due to beam loss may place severe constraints on the operation of high energy accelerators which utilize superconducting magnets. Losses on ejection septa, assuming an unbunched beam mode of operation, are unavoida...
Variability in Blazars allows important constraints on the size of emitting regions, Dopplerboost, the time-scale for particle acceleration, and loss-timescales. Since all of the above vary with energy, multifrequency studies are mandatory. Nonetheless individual events seem not to provide unique pictures. Recent advances in population ...
This Department of Energy publication considers those factors which will determine the ability of the railroads, water carriers, coal slurry pipelines, high voltage electrical transmission lines, and truck movements to meet increasing demands for coal hau...
During the last few years many suggestions have been made for novel accelerating schemes, with the aim of making centre of mass energies of 1 TeV and above available for e(+) e(-) collisions at a socially acceptable cost. A wavelength range from micromete...
Large fusion devices will almost certainly produce net energy. However, a successful commercial fusion energy system must also satisfy important engineering and economic constraints. Inertial confinement fusion power plants driven by multi-stage, heavy-ion accelerators appear capable of meeting these ...
Inertial-fusion targets were designed for use with heavy-ion accelerators as drivers in fusion energy power plants. In the interest of providing inputs for understanding the trade-offs among accelerator designs, an initial survey was carried out regarding target gain versus parameters of relevance. This was done in two stages, firstly ...
Analytical and computer simulation results are reported on the dynamics of a high current electron ring in a conventional betatron accelerator. These studies include, in addition to the external and self fields, the effects of surrounding walls and toroidal corrections. Results show that, in contrast with the modified betatron, the equilibrium in a conventional betatron is ...
The report focuses on the Federal Government, the Nation's largest single energy consumer, in terms of the opportunities and constraints for the use of energy efficient technologies. The study reviews past and current efforts to improve Federal energy efficiency and discusses policy options that could ...
... of the Russian Military: Constraints, Trends, and Factors Affecting Stability and ... by accelerating the development of those positive factors identified ...
The basic conservation laws for mass, momentum and energy along flow tubes from the sun to the Earth, together with observational constraints coming from remote sensing observations of the corona and in-situ measurements of the wind may be used to derive scaling laws relating the asymptotic solar wind properties to the source regions on the sun. This paper ...
Group 1: Electron Acceleration and Propagation. Group Leader: ... for electron propagation and acceleration; Observational and theoretical constraints on ...
Combining constraints from particle accelerators with the requirement that the ..... In the case of pseudoscalar Higgs boson exchange there are no loops of ...
... Reclamation (BUR), US Geological Service (USGS), and Bureau ... Resource Constraints ... service centers have sufficient resources to accelerate the ...
SNAP is a candidate for the Joint Dark Energy Mission (JDEM) that seeks to place constraints on the dark energy using two distinct methods. The first, Type Ia SN, is discussed in a separate white paper. The second method is weak gravitational lensing, whi...
The transverse resistive wall instability in the Two-Beam Accelerator (TBA) is investigated analytically and numerically. Without any damping mechanism, we find one to four e-folds in 100 m, depending on the design. It is found that Landau damping, due to energy spread within a beam slice, is not effective, due to rapid synchrotron oscillations in the FEL ...
The accelerators must take the muon beams from {approximately} 100 MeV to 2 TeV energies within the muon lifetime for a 4 TeV energy muon collider. These constraints plus the muon decay heating seriously challenge the designs of the superconducting RF (SRF) cavities and magnets in the ...
We simulate fusion power plant driver efficiency by pulsing small induction cores at 5 Hz (a typical projected power plant repetition rate), with a resistive load in the secondary winding that is scaled to simulate the beam loading for induction acceleration. Starting from a power plant driver design that is based on other constraints, we obtain the core ...
... were determined from energy balances on the ... TEMPERATURE, ACCELERATION, ENERGY, SURFACE ... COEFFICIENTS, BALANCE, ...
We studied depolarization mechanisms of polarized proton acceleration in high energy accelerators with snakes and found that the perturbed spin tune due to the imperfection resonance plays an important role in beam depolarization at snake resonances. We also found that even order snake resonances exist in the overlapping intrinsic and ...
Interactions between dark matter and dark energy with a given equation of state are known to modify the cosmic dynamics. On the other hand, the strength of these interactions is subject to strong observational constraints. Here we discuss a model in which the transition from decelerated to accelerated expansion of the Universe arises ...
We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of ...
This report of the Interagency Geothermal Task Force analyzes the potential production capabilities of the geothermal industry and the resources necessary to achieve these levels of production. The study covers four areas: resources exploration and assessment; environmental, legal and institutional research; resource utilization projects; and advanced research and technology efforts. The analysis ...
The model was developed in which the following dynamic mechanisms combine to create a growing gap between domestic energy demand and production: a tendency toward exponential growth in energy demand; depletion of the domestic oil and gas resource base; and delays and constraints in the development of alternative ...
Combined Cluster EFW and EDI measurements have shown that cold ion outflow in the magnetospheric lobes dominates the hydrogen ion outflow from the Earth's atmosphere. The ions have too low kinetic energy to be measurable with particle instruments, at least for the typical spacecraft potential of a sunlit spacecraft in the tenuous lobe plasmas outside a few RE. The measurement ...
The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints ar...
The matter content of relativistic jets in AGNs is dominated by a mixture of protons, electrons, and positrons. During dissipative events these particles tap a significant portion of the internal and/or kinetic energy of the jet and convert it into electromagnetic radiation. While leptons - even those with only mildly relativistic energies - can radiate ...
We use the high energy predictions of a QCD-inspired parameterization of all accelerator data on forward proton-proton and antiproton-proton scattering amplitudes, along with Glauber theory, to predict proton-air cross sections at energies near s~30 TeV. The parameterization of the proton-proton cross section incorporates analyticity ...
A 1 kW infrared FEL, funded by the U.S. Navy, is being built at Jefferson Lab. It will be driven by a compact energy-recovering CW superconducting radio-frequency (SRF)-based linear accelerator. Stringent phase space requirements at the wiggler, low beam energy, and high beam current subject the design to numerous ...
Recent progress in the understanding of beam physics and technology factors determining the current and brightness of ion and electron beams in linear accelerators will be reviewed. Topics to be discussed including phase-space density constraints of particle sources, low-energy beam transport include charge neutralization, emittance ...
Three main items in the design of large linear colliders are presented. The first is the interrelation of energy and luminosity requirements. These two items impose severe constraints on the accelerator builder who must design a machine to meet the needs of experimentl high energy physics rather than designing a ...
We consider Double Quintessence models for which the Dark Energy sector consists of two coupled scalar fields. We study, in particular, the possibility to have a transient acceleration in these models. In both Double Quintessence models studied here, it is shown that, if acceleration occurs, it is necessarily transient. We consider ...
It has been argued that the underlying acceleration mechanism in many extreme Solar Energetic Particle (SEP) events is diffusive shock acceleration. Energetic particles in these events often reach � GeV/nucleon in relatively short period of time. This places a strong constraint on the applicability of the diffusive shock ...
Current constraints on the dark energy equation of state parameter, w, are expected to be improved by more than 1 order of magnitude in the next decade. If |w-1| > or approx. 0.01 around the present time, but the dark energy dynamics is sufficiently slow, it is possible that future constraints will rule out ...
... applications; Synchrotron light sources and free electron lasers; Low and intermediate energy accelerators; High energy hadron accelerators and ...
Isotopic abundance measurements of galactic cosmic-ray Ni-59 and Co-59 will be reported from the Cosmic Ray Isotope Spectrometer (CRIS) on the NASA Advanced Composition Explorer (ACE). These nuclides form a parent-daughter pair in a radioactive decay which can occur only by electron capture, and is no longer possible once the nuclei are accelerated to high ...
The energetics of electromagnetic acceleration of ultrahigh-energy cosmic rays (UHECRs) is constrained both by confinement of a particle within an acceleration site and by radiative energy losses of the particle in the confining magnetic fields. We demonstrate that the detection of approximately 3 x 10(20) eV ...
PubMed
We make new predictions of ?p-airprod, the proton-air inelastic production cross section, at pp center-of-mass energies 0.1?s?100TeV, using high-energy predictions from a saturated Froissart bound parametrization of accelerator data on forward p�p and pp scattering amplitudes, together with Glauber theory. The parametrization of the ...
arXiv:0912.3816v1[astro-ph.CO]18Dec2009 Testable dark energy predictions from current data Michael a class of dark energy models, constraints from one set of cosmic acceleration observables make, and the Hubble constant. With a cosmological constant as the dark energy and assuming near-minimal ...
E-print Network
We compare three different methods for direct energy minimization in electronic structure calculations where the gradient of the energy functional with respect to the molecular orbitals is available. These methods make use of the preconditioned gradient to increase robustness. An orbital transformation is used to ensure that the orthogonality ...
... Title : Public Sector Investment in Energy: Budgetary Constraints and Trade Offs in Pakistan. Descriptive Note : Journal article. ...
... Accession Number : ADA528057. Title : Infrastructural Constraints on Energy Development: The Case of Pakistan. Descriptive Note : Journal article. ...
In this presentation, I shall discuss the linear collider program at the Stanford Linear Accelerator Center as it is now, and as we hope to see it evolve over the next few years. Of greatest interest to the high energy accelerator physics community gathered here is the development of the linear collider concept, and so I shall ...
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, f(G), is added to the general relativity action. We show that a theory of this kind is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence, or phantom cosmic ...
One approach for heating a target to ''Warm Dense Matter'' conditions (similar, for example, to the interiors of giant planets or certain stages in Inertial Confinement Fusion targets), is to use intense ion beams as the heating source (see refs.[6] and [7] and references therein for motivation and accelerator concepts). By consideration of ...
The electron energy distribution index, p, is a fundamental parameter of the process by which electrons are accelerated to relativistic speeds and by which they radiate, via synchrotron emission. This acceleration process is applicable to a myriad of astronomical sources, from jet sources such as AGN, X-ray binaries and gamma-ray ...
We propose a new parametrization of the deceleration parameter to study its time-variation behavior. The advantage of parameterizing the deceleration parameter is that we do not need to assume any underlying theory of gravity. By fitting the model to the 157 gold sample supernova Ia data, we find strong evidence that the Universe is currently accelerating and it ...
The injection and acceleration of thermal solar wind ions at the quasi-parallel earth's bow shock during radial interplanetary magnetic field conditions is investigated. Active Magnetospheric Particle Tracer Explorers/Ion Release Module satellite observations of complete proton spectra, and of heavy ion spectra above 10 keV/Q, made on September 12, 1984 near the nose ...
This paper describes considerations for selection of structural and target materials for accelerator-driven neutron sources. Due to the operating constraints of proposed accelerator-driven neutron sources, the criteria for selection are different than those commonly applied to fission and fusion systems. Established irradiation ...
We explore possible constraints on the inflationary equation state: p = w?. While w must be close to -1 for those modes that contribute to the observed power spectrum, for those modes currently out of experimental reach, the constraints on w are much weaker, with only w < -1/3 as an a priori requirement. We find, however, that limits on the reheat ...
The accelerator configuration that will result in the largest fraction of accelerator kinetic energy transferred to accelerated particles is explicitly determined from general principles.
The accelerator configuration that will result in the largest fraction of accelerator kinetic energy transferred to accelerated particles is explicitly determined from general principles. (ERA citation 12:009733)
We present constraints on the cosmic growth history with recent cosmological data, allowing for deviations from {Lambda}CDM as might arise if cosmic acceleration is due to modifications to general relativity or inhomogeneous dark energy. We combine measures of the cosmic expansion history, from Type 1a supernovae, baryon acoustic ...
In an undulant universe, cosmic expansion is characterized by alternating periods of acceleration and deceleration. We examine cosmologies in which the dark-energy equation of state varies periodically with the number of e-foldings of the scale factor of the universe, and use observations to constrain the frequency of oscillation. We find a tension between ...
The authors present recent measurements of the CKM angle {alpha} using data collected by the BABAR detector at the PEP-II asymmetric-energy e{sup +}e{sup -} collider at the SLAC National Accelerator Laboratory, operating at the {Upsilon}(4S) resonance. They present constraints on {alpha} from B {yields} {pi}{pi}, B {yields} {rho}{rho} ...
Six papers are included in this collection. They cover: a second interaction region for gamma-gamma, gamma-electron and electron- electron collisions; constraints on laser-driven accelerators for a high-energy linear collider; progress on the design of a high luminosity muon-muon collider; RF power source development at the RTA test ...
The energy transport in the electron-proton solar wind will be examined. An overview of the fundamental problems of solar wind heating and acceleration will be given. It will be followed by a detailed analysis of the solar wind energy budget, from the mid-chromosphere to the earth's orbit. Emphasis will be placed on the transition ...
We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint is that the radial coordinate basis vector is a unit vector field in the comoving coordinate system. We find that the ...
An account is given of the numerous uses of solid rocket propellant energy in submunition dispersion tasks under a variety of flight conditions. Among these applications are 'smart' ignition systems, gas energy management systems, and submunition packagings that employ rapidly inflating bags to shape expanding gas energy within tight ...
The potential benefits from heavy ion inertial fusion motivate the rapid development of a program to test the principle. To define the program, accelerator parameters which have not hitherto been commonly considered must be studied interactively with basic questions of space charge limitations and charge exchange. Beam lifetime and power output efficiency may ultimately lead ...
Interplanetary shocks in the heliosphere provide excellent test cases for the simulation and theory of particle acceleration at shocks thanks to the presence of in-situ measurements and a relatively well understood initial particle distribution. The Monte-Carlo test particle simulation employed in this work has been previously used to study injection and ...
... ADA438929. Title : BAMBOO: Accelerating Closed Itemset Mining by Deeply Pushing the Length-Decreasing Support Constraint. ...
The international accelerator school on Frontiers of Accelerator TechnoIogy was organized jointly by the US Particle Accelerator School (Dr. Mel Month and Ms. Marilyn Paul), the CERN Accelerator School, and the KEK Accelerator School, and was hosted by th...
The modelling of earthquake loads as design inputs for inelastic single-degree-of-freedom structures is considered. The earthquake load is modelled as a deterministic time history which is expressed in terms of a Fourier series that is modulated by an enveloping function. Subsequently, the coefficients of the series representation, and, the parameters of the envelope function are determined such ...
Observed disparities between in situ observations and current theories of charged-particle acceleration suggest that the acceleration of these particles in space is more complicated than previously thought. In its simplest form, the long-favored model of diffusive shock acceleration at a steady, planar shock is clearly inadequate. ...
Future Accelerators, was created to facilitate international collaboration in the construction and use of accelerators for high energy physics. It was created in 1976 by the...
Science.gov Websites
... warfare, joint planning, national and international ... ACCELERATORS, LINEAR ACCELERATORS, PARTICLE ACCELERATOR TARGETS ...
The Pierce design acceleration column has been widely used to accelerate high current beams. It operates well in the space charge limited condition, and will produce beams with a temperature comparable with that of the source. It is restricted in current density, however, by the Child-Langmuir relation. If the ion source itself is not the limiting ...
Different theoretical models of particle acceleration in solar flares predict different accelera-tion/injection sites in flaring loops, as well as different pitch-angle distributions of accelerated electrons. In this study we solve the non-stationary Fokker-Plank kinetic equation with differ-ent assumptions on the injection site and pitch-angle anisotropy ...
The next generation of accelerators and ever expanding needs of existing accelerators demand new developments and additions to Monte-Carlo codes, with an emphasis on enhanced modeling of elementary particle and heavy-ion interactions and transport. Challenges arise from extremely high beam energies and beam power, increasing complexity ...
A two-fluid hydrodynamical model governing the transport of cosmic rays in a relativistically moving
NASA Technical Reports Server (NTRS)
Using the radio through hard X-ray images of the Crab nebula to derive the spatial dependence of the
... _ i_ i NADC-MR-7015 2 July 1970 Activation Energies of Acceleration and Hypoxia Stress ... Activation Energies of Acceleration and Hypoxia Stress ...
The authors explore the multidimensional space of beam parameters, looking for preferred regions of operation for a e{sup +}e{sup {minus}} linear collider at 5 TeV center of mass energy. Due to several major constraints such a collider is pushed into certain regime of high beamstrahlung parameters, {Upsilon} regime is examined with IP simulations using the ...
The centerpieces of the Los Alamos Neutron Science Center (LANSCE) are a half-mile long 800-MeV proton linear accelerator and proton storage ring. The accelerator, storage ring, and target stations provide the protons and spallation neutrons that are used in the numerous basic research and applications experimental programs supported by the US Department ...
This paper presents a preliminary investigation on energy harvesting from human walking via piezoelectric vibrating cantilevers. Heel accelerations during human gait are established by correlating data gathered from the literature with direct experimental measurements. All the observed relevant features are synthesized in a typical (standard) ...
The accelerating expansion of our Universe at present could be driven by an unknown energy component (dark energy) or a modification of general relativity (modified gravity). In this paper we revisit the constraints on a phenomenological model which interpolates between the pure {lambda}CDM model and the ...
A precise determination, and comparison, of the epoch of the onset of cosmic acceleration, at redshift z{sub acc}, and of dark energy domination, at z{sub eq}, provides an interesting measure with which to parametrize dark energy models. By combining several cosmological data sets, we place constraints on the ...
High-energy particle acceleration is observed to proceed in a diverse variety of astrophysical sites
... Descriptors : *ELECTRON ACCELERATORS, *LINEAR ACCELERATORS, ELECTROMAGNETIC FIELDS, SCATTERING, ENERGY ...
In this paper, we use the type Ia supernovae data to constrain the holographic dark energy model proposed by Li. We also apply a cosmic age test to this analysis. We consider in this paper a spatially flat Friedmann-Robertson-Walker universe with a matter component and a holographic dark energy component. The fit result shows that the case c<1 (c=0.21) ...
Modified gravity, known as f(R) gravity, has presently been applied to cosmology as a realistic alternative to dark energy. For this kind of gravity the expansion of the Universe may accelerate while containing only baryons and dark matter. The aim of the present investigation is to place cosmographic constraints on the class of ...
The spectra of galactic cosmic rays that are observed inside the heliosphere result from the interaction of the spectra present in the local interstellar medium with the structured but turbulent magnetic field carried by the solar wind. Observational tests of solar modulation theory depend on comparisons between spectra inside and outside the heliosphere. Our knowledge of the local interstellar ...
Cosmic parallax is the change of angular separation between a pair of sources at cosmological distances induced by an anisotropic expansion. An accurate astrometric experiment like Gaia could observe or put constraints on cosmic parallax. Examples of anisotropic cosmological models are Lemaitre-Tolman-Bondi void models for off-center observers (introduced to explain the ...
A central issue in the energy policymaking arena today is the timing and method of the decontrol of natural gas prices. Current policy dictates a phased deregulation of natural gas prices with a complete lifting of price controls to occur in 1985. Various policy actions being contemplated involve both an accelerated phased decontrol scenario and an ...
Very high energy (VHE, >100 GeV) ?-rays are expected to be emitted from the vicinity of supermassive black holes (SMBHs), irrespective of their activity state. In the magnetosphere of rotating SMBH, efficient acceleration of charged particles can take place through various processes. These particles could reach energies up to E ~ ...
In some classes of inflationary models, a violation of the null energy condition (NEC) is expected during the phase of accelerated expansion. The most striking observational effect would be a "blue" spectrum of primordial gravitational waves with a spectral index nT larger than zero. In this brief paper, we first update the current ...
A computer model for systems analysis of heavy ion drivers based on induction linac technology has been used to evaluate driver designs for inertial fusion energy (IFE). Design parameters and estimated costs have been determined for drivers with various ions, different charge states, different front-end designs, with and without beam merging, and various pulse compression and ...
In recent years, the quark-mixing angles and the CP phase in the Cabibbo-Kobayashi-Maskawa matrix have been measured with very high precision. Today, the availability of high-luminosity hadronic and electron-positron accelerators enables indirect searches for new quark generations and interactions at energies in the TeV range via rare processes involving ...
Experimental and theoretical high-energy physics research at Purdue is summarized in a number of reports. Subjects treated include the following: the CLEO experiment for the study of heavy flavor physics; gas microstrip detectors; particle astrophysics; affine Kac-Moody algebra; nonperturbative mass bounds on scalar and fermion systems due to triviality and vacuum stability ...
We propose a model based on a DBI action for the unification of dark matter and dark energy. This is supported by the results of the study of its background behavior at early and late times, and reinforced by the analysis of the evolution of perturbations. We also perform a Bayesian analysis to set observational constraints on the parameters of the model ...
The idea that we live near the center of a large, nonlinear void has attracted attention recently as an alternative to dark energy or modified gravity. We show that an appropriate void profile can fit both the latest cosmic microwave background and supernova data. However, this requires either a fine-tuned primordial spectrum or a Hubble rate so low as to rule these models ...
The wakefield accelerator concept consists of utilizing the electric field generated by the motion of one group of particles to accelerate another group of particles. Essentially, the wakefield accelerator is a transformer which transfers the energy in a ...
Recent developments in the technology of electrostatic accelerators, linear accelerators, and cyclotrons for the acceleration of heavy ions are reviewed. (GHT)
Recent developments in the technology of electrostatic accelerators, linear accelerators, and cyclotrons for the acceleration of heavy ions are reviewed. (ERA citation 04:047251)
The apparatus is for phasing a linear accelerator waveguide section. The system is useful for phasing very long accelerators. The phase relation of the electromagnetic energy at different points in each accelerator section is utilized.