AC Dipole Research Articles

Measurement of the Magnetic and Thermal Characteristics of Ferrites for a 300 kHz AC Dipole for the Mu2e Experiment

A charged lepton flavor violation experiment, Mu2e, is planned at Fermilab, searching for muon to electron conversions with an unprecedented sensitivity, better than 6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> at 90% CL. To achieve such sensitivity the incoming beam must be highly suppressed during the window for detecting the conversion a muon into an electron. One proposal for beam extinction is based on a collimator with two dipoles running in a resonant circuit at ~300 kHz synchronized to the bunch spacing. An appropriate choice of the ferrite material for the magnet yoke is critical to ensuring the reliable operation of such a high frequency dipole over the life of the experiment. In this paper, we present the results of the thermal and magnetic measurements of the selected ferrite material, including the field non-linearity effects and power losses. Some dimensional optimization of the ferrite bricks is also discussed.

Dielectrophoresis of ionized gas microbubbles: Dipole reversal due to diffusive double-layer polarization

Gas bubbles generated by electrolysis reactions are shown to exhibit anomalous induced ac dipoles and dielectrophoretic behavior that cannot be described by classical Maxwell–Wagner theory. Normal charging and screening of conducting ionized gas in the gas-phase double layer are shown to render the bubble insulating at low ac field frequencies to affect negative dielectrophoresis. This screening effect couples with dielectric polarization at high frequencies to produce no crossover frequency for small bubbles and two crossover frequencies for bubbles larger than a critical size of 40 μm. A double-layer theory accurately captures the two crossover frequencies and critical bubble size behavior.

Parametrization of the driven betatron oscillation

An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam oscillations in a synchrotron. By observing this driven coherent oscillation, the linear optical parameters can be directly measured at locations of the beam position monitors. The driven oscillations induced by an AC dipole will generate a phase space ellipse which differs from that of free oscillations. If not properly accounted for, this difference can lead to misinterpretations of the actual optical parameters, for instance, 6% or more in the cases of the Tevatron, RHIC, or LHC. This paper shows that the effect of an AC dipole on the observed linear optics is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. The introduction of this new amplitude function also helps measurements of the normal Courant-Snyder parameters based on beam position data taken under the influence of an AC dipole. This new parametrization of driven oscillations is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.

Measurement of IR optics with linear coupling’s action-angle parametrization

Linear coupling's action-angle parametrization is convenient for interpretation of turn-by-turn beam position monitor (BPM) data. We demonstrate how to apply this parametrization to extract Twiss and coupling parameters in interaction regions (IRs), using BPMs on each side of a long IR drift region. Example data were acquired at the Relativistic Heavy Ion Collider, using an ac dipole to excite a single transverse eigenmode. We have measured the waist of the $\ensuremath{\beta}$ function and its Twiss and coupling parameters.

Induced dipole effect in strong-field photodetachment of atomic negative ions

The process of strong-field photodetachment of an atomic negative ion is considered with a simple analytical account for the ac dipole moment induced in the atomic core by the external laser field. The method is based on a Keldysh-like saddle-point theory, modified by using dipole-spherical angular wave functions in the initial state of the outer electron. The field-induced dipole results in an increase of the detachment rate and essential modifications in its angular dependence. These modifications are interpreted as destruction of the quantum interference originated from the coherent superposition of the two saddle-point contributions to the transition amplitude.

Measurement of global and local resonance terms

Recently, resonance driving terms were successfully measured in the CERN SPS and the BNL RHIC from the Fourier spectrum of beam position monitor (BPM) data. Based on these measurements a new analysis has been derived to extract truly local observables from BPM data. These local observables are called local resonance terms since they share some similarities with the global resonance terms. In this paper we derive these local terms analytically and present experimental measurements of sextupolar global and local resonance terms in RHIC. Nondestructive measurements of these terms using ac dipoles are also presented.

Adiabaticity of the ramping process of an ac dipole

ac dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. If the excitation amplitude is slowly increased to the desired value and slowly decreased back to zero there is no significant emittance growth. The aim of this article is to study the adiabaticity of the ramping process of an ac dipole as a function of the different parameters involved.

Ultrastable optical clock with neutral atoms in an engineered light shift trap.

An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).

Normal form of particle motion under the influence of an ac dipole

AC dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. These beam oscillations may last arbitrarily long and, in principle, there is no significant emittance growth if the AC dipole is adiabatically turned on and off. Therefore the AC dipole seems to be an adequate tool for non–linear diagnostics provided the particle motion is well described in presence of the AC dipole and non–linearities. Normal Forms and Lie algebra are powerful tools to study the non–linear content of an accelerator lattice. In this article a way to obtain the Normal Form of the Hamiltonian of an accelerator with an AC dipole is described. The particle motion to first order in the non– linearities is derived using Lie algebra techniques. The dependence of the Hamiltonian terms on the longitudinal coordinate is studied showing that they vary differently depending on the AC dipole parameters. The relation is given between the lines of the Fourier spectrum of the turn–by–turn motion and the Hamiltonian terms.

Focus on Magnetics

Focus on Magnetics

Extracting Classical Trajectories from Atomic Spectra

We describe how to reconstruct individual classical trajectories from spectroscopic data. The ac dipole moment of a trajectory can be found from the effect of an oscillating field on the spectrum. The inverse Fourier transform of such data yields the component of the electron trajectory along the direction of the oscillating field. We demonstrate the method by experimentally extracting $z(t)$ for two electron trajectories that influence the Stark spectrum of Rydberg lithium. Within the experimental resolution, the reconstructed orbits agree well with classical predictions.

Determination of positions, velocities, and kinetic energies of resonantly excited ions in the quadrupole ion trap mass spectrometer by layer photodissociation

The effects on ion motion caused by the application of a resonance AC dipole voltage to the end-cap electrodes of the quadrupole ion trap are described. An excimer laser is used to photodissociate benzoyl ions, and its triggering is phase locked to the AC voltage to follow the motion of the ion cloud as a function of the phase angle of the AC signal. Resonantly excited ions maintain a coherent motion in the presence of He buffer gas, which dissipates energy from the ions via collisions. Maximum ion displacements, which depend upon the potential well depth ( q z value), occur twice each AC cycle. Axial components of ion velocities are determined by differentiating the displacements of the distributions with respect to time. The experimental data show that these velocities are maximized when the ion cloud passes through zero axial displacement, and they compare favorably with results calculated using a simple harmonic oscillator model. Axial components of ion kinetic energies are low (< 5 eV) under the chosen experimental conditions. At low values of q z (~0.2), the width of the ion distribution increases as the ion cloud approaches the center of the trap and decreases as it approaches the end-cap electrodes. This effect is created by compaction of the ion trajectories when ion velocities are decreased.

Dynamo models with permanent dipole fields and secular variation

The long‐term behavior of azimuthally averaged core magnetic fields is examined using numerical calculations of nonlinear, axisymmetric, kinematic α2 and α2ω dynamos. The important elements of the model are convective turbulence, parameterized by an α effect, and a toroidal shear flow, providing the ω effect. Magnetic fields produced by this model exhibit several styles of behavior. For Rα Rω &lt; 0, where Rα and Rω, are the amplitudes of the α effect and ω effect in the northern hemisphere, the dipolar component of the field is found to be oscillatory (ac). For Rα Rω &gt; 0, we identify three regimes of field behavior corresponding to the magnitude of Rω Small Rω values produce nonoscillatory (dc) dipolar fields with zero quadrupolar components, while large values of Rω, produce ac dipole and ac quadrupole fields. Intermediate values of Rω produce fields with dc dipole components coexisting with poleward propagating αω dynamo waves in the quadrupole family. This regime of field behavior is most consistent with the observed behavior of the Earth's paleomagnetic field on the 103–104 year time scale of paleomagnetic secular variation.