Focusing a fountain of neutral cesium atoms with an electrostatic lens triplet

An electrostatic lens with three focusing elements in an alternating-gradient configuration is used to focus a fountain of cesium atoms in their ground (strong-field-seeking) state. The lens electrodes are shaped to produce only sextupole plus dipole equipotentials which avoids adding the unnecessary nonlinear forces present in cylindrical lenses. Defocusing between lenses is greatly reduced by having all of the main electric fields point in the same direction and be of nearly equal magnitude. The addition of the third lens gave us better control of the focusing strength in the two transverse planes and allowed focusing of the beam to half the image size in both planes. The beam envelope was calculated for lens voltages selected to produced specific focusing properties. The calculations, starting from first principles, were compared with measured beam sizes and found to be in good agreement. Application to fountain experiments, atomic clocks, and focusing polar molecules in strong-field-seeking states is discussed.Comment: 8 pages 10 figure

Electrostatic end-field defocusing of neutral atoms and its compensation

Neutral atoms entering an electric field experience a defocusing force in the dipole field direction, which is proportional to the field gradient. If an experiment, such as the search for a permanent electron electric dipole moment (eEDM), requires a very strong electric field (13.5  MV/m), then this end-field defocusing results in beam blowup and much reduced phase-space acceptance. In this paper we discuss how these defocusing fields arise from the longitudinal changes in the electric dipole field and their dependence on the electrode shape and spacing between lenses. We find that the end-field defocusing comes from strong impulse forces, whose defocusing power was calculated for simple electrodes with rounded ends. To compensate for this end-field defocusing, a triplet of transverse-focusing lenses was added to the pure dipole field plates in the generic eEDM cesium fountain experiment used to study the neutral beam optics. Envelope equations, which calculated the beam sizes of the atom bunch for the linear forces, are used to obtain a set of lens parameters that give a well focused beam in the fountain. Atom trajectory equations allow us to calculate the phase-space acceptance of the lens system with the nonlinear force terms included

Statistical-Mechanical Studies of the α ⇄ β Transformation in Keratins: II. The Tension-Length Isotherms

In attempting to understand the yield region of the α ⇄ β transformation in keratins (Astbury and Woods, 1933), we recently proposed a statistical-mechanical model (David and Schor, 1965) which generalized the work done by others on the helix ⇄ random coil transformation (Zimm and Bragg, 1959; Gibbs and DiMarzio, 1959) (thermal denaturation) to the case of a polypeptide under external tension (Birstein, 1962). We wish now to report the comparison of the quantitative aspects of this model to the observed tension-length isotherms (in the yield region) of Cotswold wool