Microwave growth from the beam breakup instability in long‐pulse electron beam experiments

The beam breakup (BBU) instability has been investigated in high‐current, long‐pulse electron beams propagating through microwave cavities. Experiments are performed using a relativistic electron‐beam generator with diode parameters: 0.7–0.8 MV, 1–15 kA, and 0.5–1.5 μs. The magnitude of the solenoidal magnetic field places these experiments in an intermediate regime between strong focusing and weak focusing. The electron‐beam transport system consists of ten identical pillbox cavities each containing a small microwave loop antenna designed to detect the TM110 beam breakup mode. The TM110 microwave mode is primed in the first cavity by a magnetron tuned to the resonance frequency of 2.5 GHz. The BBU instability growth is measured through the amplification of the 2.5 GHz microwaves between the second and tenth cavities. Strong growth (25–38 dB) of the TM110 microwave signal is observed when the initial cavity is primed exactly on resonance, with a rapid decrease of the growth rate off‐resonance. The magnitude of microwave growth is consistent with the predictions of BBU theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69350/2/APPLAB-61-6-642-1.pd

The beam breakup instability in quadrupole and solenoidal electron‐beam transport systems

Dispersion relations are derived to determine the growth rate, dominant wavelength, and group velocity of disturbances caused by the beam breakup instability. Considerations include weak and strong focusing, x‐y coupling in solenoidal transport, the spacing of accelerator cavities, and periodically pulsed beams. Beam breakup growth is minimum when the cavity spacing equals an integral number of half‐betatron wavelengths for quadrupole focusing, and an integral number of betatron wavelengths for solenoidal focusing. Minimum growth is also found for periodic pulses separated by an integral number of half‐periods of the TM110 cavity mode. Expressions for beam breakup growth at the minima are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71286/2/JAPIAU-71-7-3091-1.pd

Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Beam breakup growth and reduction experiments in long‐pulse electron beam transport

The results of an experimental program whose sole objective is to investigate the cumulative beam breakup instability (BBU) in electron beam accelerators are presented. The BBU growth rate scalings are examined with regard to beam current, focusing field, cavity Q, and propagation distance. A microwave cavity array was designed and fabricated to excite and measure the cumulative BBU resulting from beam interactions with the deflecting TM110 cavity mode. One phase of this experiment used high Q(≊1000) cavities with relatively large frequency spread (Δf/f0≊0.1%). The observed TM110 mode microwave growth between an upstream (second) and a downstream (tenth) cavity indicated BBU growth of 26 dB for an electron beam of kinetic energy of 750 keV, 45 A, and focused by a 1.1 kG solenoidal field. At beam currents of less than 100 A the experiments agreed well with a two‐dimensional continuum theory; the agreement was worse at higher beam currents (≳100 A) due to beam loading. The second‐phase experiments used lower Q(≊200) cavities with relatively low frequency spread (Δf/f0≊0.03%). Theory and experiment agreed well for beam currents up to 220 A. Distance scaling experiments were also performed by doubling the propagation length. Instability growth reduction experiments using the technique of external cavity coupling resulted in a factor of four decrease in energy in BBU growth when seven internal beam cavities were coupled by microwave cable to seven identical external dummy cavities. A theory invoking power sharing between the internal beam cavities and the external dummy cavities was used to explain the experimental reduction with excellent agreement using an equivalent circuit model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71080/2/JAPIAU-75-3-1258-1.pd

Measurement of long‐pulse relativistic electron beam perpendicular‐ to‐parallel velocity ratio by Cerenkov emission and radiation darkening on a glass plate

We report measurements of the ratio of the perpendicular velocity to the parallel velocity, α= v⊥ /v∥, of a relativistic electron beam gyrating in a magnetic field by the use of (1) Cerenkov emission from a glass plate, detected by a gated microchannel plate image intensifier camera, and (2) electron‐beam‐induced radiation darkening pattern on the same glass plate. The measurements are based on a direct determination of the Larmor radius of an electron beam of known energy. Experiments were performed on a long‐pulse electron beam accelerator with e‐beam diode parameters: VD = 0.6–0.9 MV, pulse length=0.5–1 μs, ID = 1–10 kA. The experimental value of α agrees with simulation results from particle trajectory codes as well as theoretical predictions from Busch’s theorem and adiabatic theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70360/2/RSINAK-63-2-1671-1.pd

Radio frequency plasma processing effects on the emission characteristics of a MeV electron beam cathode

Experiments have proven that surface contaminants on the cathode of an electron beam diode influence electron emission current and impedance collapse. This letter reports on an investigation to reduce parasitic cathode current loss and to increase high voltage hold off capabilities by reactive sputter cleaning of contaminants. Experiments have characterized effective radio frequency (rf) plasma processing protocols for high voltage anode–cathode (A–K) gaps using a two-stage argon/oxygen and argon rf plasma discharge. Time-resolved optical emission spectroscopy measures contaminant (hydrogen) and bulk cathode (aluminum) plasma emission versus transported axial electron beam current turn on. Experiments were performed at accelerator parameters: V = −0.7V=−0.7 to −1.1 MV,−1.1MV, I(diode)=3–30 kA,I(diode)=3–30kA, and pulse length=0.4–1.0 μs.length=0.4–1.0μs. Experiments using a two-stage low power (100 W) argon/oxygen rf discharge followed by a higher power (200 W) pure argon rf discharge yielded an increase in cathode turn-on voltage required for axial current emission from 662±174 kV662±174kV to 981±97 kV.981±97kV. The turn-on time of axial current was increased from 100±22100±22 to 175±42 ns.175±42ns. © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69353/2/APPLAB-75-1-31-1.pd

Deflection of carbon dioxide laser and helium‐neon laser beams in a long‐pulse relativistic electron beam diode

Deflection of carbon dioxide and helium‐neon laser beams has been used to measure plasma and neutral density gradients during the operating mode and after the shorting time of a long‐pulse field‐emission electron beam diode. Plasma density gradients of (1014–1015) cm−4 were observed throughout the diode during the final microsecond of the 2–3 μs electron beam pulse. The neutral density gradient was less than 1×1018 cm−4 during the electron beam pulse. Upon diode shorting, neutral density gradients increased to (1018–1019) cm−4 over ∼1 μs, and decayed over many microseconds. Plasma density gradients of ∼1015 cm−4 were also observed after shorting. These experiments demonstrate the value of carbon‐dioxide laser and helium‐neon laser deflection for diagnosing plasma and neutral particles in long‐pulse electron beam diodes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70220/2/RSINAK-62-7-1776-1.pd

Histamine as a marker for hydroxyl radicals

During inflammation an influx of neutrophils and release of mediators from mast cells (such as histamine) take place. The stimulated neutrophils can produce reactive oxygen species (ROS). One of these ROS is the highly reactive hydroxyl radical (OH.). It would be interesting to be able to quantify the extent of ROS formation. We investigated if histamine which is present at the inflammation site can serve as an endogenous marker for the formation of OH.. We found that histamine after incubation with OH. gave two distinct products in our HPLC system. One of the products gave the same characteristics as the synthesized 2-imidazolone derivative of histamine. This suggests that this derivative will be formed when histamine is incubated with OH.

Temporal and spatial variability in stable isotope ratios of SPM link to local hydrography and longer term SPM averages suggest heavy dependence of mussels on nearshore production

Temporal changes in hydrography affect suspended particulate matter (SPM) composition and distribution in coastal systems, potentially influencing the diets of suspension feeders. Temporal variation in SPM and in the diet of the mussel Perna perna, were investigated using stable isotope analysis. The δ13C and δ15 N ratios of SPM, mussels and macroalgae were determined monthly, with SPM samples collected along a 10 km onshore–offshore transect, over 14 months at Kenton-on-Sea, on the south coast of South Africa. Clear nearshore (0 km) to offshore (10 km) carbon depletion gradients were seen in SPM during all months and extended for 50 km offshore on one occasion. Carbon enrichment of coastal SPM in winter (June–August 2004 and May 2005) indicated temporal changes in the nearshore detrital pool, presumably reflecting changes in macroalgal detritus, linked to local changes in coastal hydrography and algal seasonality. Nitrogen patterns were less clear, with SPM enrichment seen between July and October 2004 from 0 to 10 km. Nearshore SPM demonstrated cyclical patterns in carbon over 24-h periods that correlated closely with tidal cycles and mussel carbon signatures, sampled monthly, demonstrated fluctuations that could not be correlated to seasonal or monthly changes in SPM. Macroalgae showed extreme variability in isotopic signatures, with no discernable patterns. IsoSource mixing models indicated over 50% reliance of mussel tissue on nearshore carbon, highlighting the importance of nearshore SPM in mussel diet. Overall, carbon variation in SPM at both large and small temporal scales can be related to hydrographic processes, but is masked in mussels by long-term isotope integration

Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field theories at weak (Hartree-Fock) and strong (Hubbard-III) coupling the expansion represents a universal and comprehensive tool for systematic improvements of static mean-field theories. As an example of the general formalism we investigate in detail an analytically tractable series of ring diagrams that correctly capture dynamical fluctuations at weak coupling. We introduce renormalizations of the diagrammatic expansion at various levels and show how the resultant theories are related to other approximations of similar origin. We demonstrate that only fully self-consistent approximations produce global and thermodynamically consistent extensions of static mean field theories. A fully self-consistent theory for the ring diagrams is reached by summing the so-called noncrossing diagrams.Comment: 17 pages, REVTEX, 13 uuencoded postscript figures in 2 separate file