Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by n _zω _z + n ₊ω ₊ + n _-ω _- = 0, where ω _z, ω ₊ and ω _- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential. Received 5 August 2002 / Received in final form 14 October 2002 Published online 17 December 2002 RID="a" ID="a"Present address: Dept. of Physics, Rampurhat College, Rampurhat, Birbhum, West Bengal, India. RID="b" ID="b"e-mail: werth@mail.uni-mainz.de     

Operation of a planar Penning trap

We demonstrate experimentally the confinement of electrons in a novel planar Penning trap. Measurement of the eigenfrequencies of the trapped electron cloud exhibits similar behaviour as in conventional 3-dimensional penning traps. The trap may be of future use in quantum computing schemes using single cold electrons.     

Calculating damping effects for the ion motion in a Penning trap

In this note a simple idea is suggested to calculate the effect of damping on the ion motion in a Penning trap. The analysis is restricted to the experimentally important special case that the axial motion (z-direction) is not coupled to that in the xy-plane, so that both motions can be treated separately. The method views the cyclotron frequency ω_c as a complex variable that can be continued analytically from real values (undamped case) into the complex plane. The power of the approach becomes obvious in connection with advanced problems such as the calculation of line profiles for quadrupole excitation.     

Determination of the helium-4 mass in a Penning trap

The determination of the rotational quadrupole alignment of diatomic molecules via REMPI detection is investigated. In this process a high focal intensity usually increases the detection probability. At high intensities the AC Stark effect may cause a splitting of the normally degenerate m_J sublevels of a rotational state J beyond the spectral width of the exciting radiation. This leads to a selective detection of only certain m_J states with the consequence that deduced alignment factors can be misleading. From the theoretical considerations line profiles are explicitly calculated for dynamic polarizabilities which represent the B ¹Σ⁺ _u←X ¹Σ⁺ _g transition of H₂, in order to fit an experimental (3+1) REMPI spectrum and to predict (1+1') line shapes as a function of laser intensity. It is further shown that the deduced quadrupole alignment factor A ₀ ⁽²⁾ is significantly changed by the second order AC Stark effect when the intensities are chosen high enough to observe asymmetric broadened line profiles. Different combinations of relative linear polarizations of the exciting and ionizing laser beams are discussed. Received 1st August 2000 and Received in final form 2 May 2001     

A new determination of the 4 He and 3 He masses in a Penning trap

The atomic and nuclear masses of ⁴He and ³He have been measured using doubly charged ions in a Penning trap connected to an electron beam ion source. Recent technical improvements allow mass determinations with uncertainties of a few parts in 10¹⁰. The obtained atomic masses are 4.002 603 256 8(13) u and 3.016 029 323 5(28) u respectively. These values deviate by as much as 5 standard deviations from the accepted values. Received 23 October 2000 and Received in final form 6 February 2001     

Dynamics of a single ion in a perturbed Penning trap. Sextupolar perturbation

In the frame work of classical mechanics, we study the nonlinear dynamics of a single ion trapped in a Penning trap perturbed by an electrostatic sextupolar perturbation. The perturbation is caused by a deformation in the configuration of the electrodes. By using a Hamiltonian formulation, we obtain that the system is governed by three parameters: the z-component of the canonical angular momentum P _φ - which is a constant of the motion because the perturbation we assume is axial-symmetric -, the parameter δ that determines the ratio between the axial and the cyclotron frequencies, and the parameter a which indicates how far from the ideal design the electrodes are. We study the case P _φ = 0. By means of surfaces of section, we show that the phase space structure is made of three fundamental families of orbits: arch, loop and box orbits. The coexistence of these kinds of orbits depends on the parameter δ. The escape is also explained on the basis of the shape of the potential energy surface as well as of the phase space structure. Received 6 September 2001 / Received in final form 19 March 2002 Published online 28 June 2002     

Thermodynamics of ionization and dissociation in hydrogen plasmas including fluctuations and magnetic fields

Applying Gibb's geometrical methods to the thermodynamics of H-plasmas we explore the landscape of the free energy as a function of the degrees of ionization and dissociation. Several approximations for the free energy are discussed. We show that in the region of partial ionization/dissociation the quantum Debye-Hückel approximation (QDHA) yields a rather good but still simple representation which allows to include magnetic field and fluctuation effects. By using relations of Onsager-Landau-type the probability of fluctuations and ionization/dissociation processes are described. We show that the degrees of ionization/dissociation are probabilistic quantities which are subject to a relatively large dispersion. Magnetic field effects are studied. Received 10 September 2002 / Received in final form 26 November 2002 Published online 11 February 2003     

On existence of the spatial charge layers in plasma with regions of rapid growth of the ionization rate

1D quasi-static self-consistent model of nonequilibrium nitrogen and oxygen plasma with highly non-uniform spatial distribution of the electric field strength is used for analysis of the correlation of ionization rate profile and charged particles profiles. It is shown that inside a region of local increase of the ionization rate the layers with violation of quasi-neutrality can exist. This leads to the appearance of local static electric fields. Special attention is devoted to plasma resonance regions in microwave plasma. The role of negative ions is also studied.     

Sum rule for the optical absorption of an interacting many-polaron gas

A sum rule for the first frequency moment of the optical absorption of a many-polaron system is derived, taking into account many-body effects in the system of constituent charge carriers of the many-polaron system. In our expression for the sum rule, the electron-phonon coupling and the many-body effects in the electron (or hole) system formally decouple, so that the many-body effects can be treated to the desired level of approximation by the choice of the dynamical structure factor of the electron (hole) gas. We calculate correction factors to take into account both low and high experimental cutoff frequencies. Received 26 April 2000 and Received in final form 5 December 2000     

A fluid model of the current-voltage characteristics of an electron emitting electrode immersed in a two electron temperature plasma

The current voltage characteristics of a negatively biased electron emitting electrode immersed in a two-electron temperature plasma are analyzed by a simple one dimensional fluid model. Based on the assumption that the electron density in the pre-sheath region obeys the Boltzmann law the Bohm criterion is derived in the form of a transcendental equation for the Mach number, which can have up to 3 solutions. According to these solutions the ion velocity at the sheath edge can be determined either by the hot or by the cool electron temperature. When it is determined by the cool electron temperature and the hot electron temperature is high enough the critical electron emission current from the collector can have a very pronounced local maximum and a minimum when regarded as a function of the electrode potential. Because of that the current voltage characteristics of the electrode may exhibit up to 3 different floating potentials. This result is in good agreement with the experimental observations reported in [J. Appl. Phys. 63, 5674 (1988)].     

Collisional damping of giant monopole and quadrupole resonances

Collisional damping widths of giant monopole and quadrupole excitations for ¹²⁰Sn and ²⁰⁸Pb at zero and finite temperatures are calculated within Thomas-Fermi approximation by employing the microscopic in-medium cross-sections of Li and Machleidt and the phenomenological Skyrme and Gogny forces, and are compared with each other. The results for the collisional widths of giant monopole and quadrupole vibrations at zero temperature as a function of the mass number show that the collisional damping of giant monopole vibrations accounts for about 30 - 40% of the observed widths at zero temperature, while for giant quadrupole vibrations it accounts for only 20 - 30% of the observed widths at zero temperature. Received: 9 January 2001 / Accepted: 29 March 2001     

Solvation and chemical reaction of sodium in water clusters

Na_m(H₂O)_n Clusters ( n = 1...200, m = 1...50) are formed in a recently build pick-up arrangement. Preformed water clusters traverse a sodium oven, where sodium atoms are picked up. At low sodium vapour pressure ( < 1×10^-4 mbar) pure Na(H₂O)_n clusters are observed in the mass spectra. At high sodium vapour pressure ( > 1×10^-3 mbar) the water cluster pick up more than 50 Na atoms and reaction products Na(NaOH)_n ( n = 2, 4...50) dominate the mass spectra. The even number of NaOH units in the products indicate that also in a finite cluster the reaction occurs in pairs as in the macroscopic reaction. Received 4 December 2000     

Search for narrow dibaryon resonances in neutral pion photoproduction from the deuteron

The reaction γd↦π⁰ X has been measured with TAPS at MAMI in the energy range E _γ = 140-300 MeV. Using the Glasgow tagging spectrometer a photon energy resolution of 0.8 MeV was achieved. The energy excitation functions of integral and differential total cross-sections show no structures of statistical significance > 2σ. Upper limits for the production of narrow isoscalar or isovector dibaryons with masses m? 2100 MeV/c² were deduced. They are in the range 2-5 μb averaged over the 0.8 MeV energy resolution. Received: 25 October 2000 / Accepted: 24 November 2000     

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a spiral spin configuration with characteristic wave vector Q different in general from the antiferromagnetic wave vector Q _AF, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a closed system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a hybrid form between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-T _c materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions. Received 15 September 2000     

ππ scattering and the meson resonance spectrum

A ππ, ˉKK, and ρρ(ωω) fully coupled channel model is used to predict the lowest isospin S, P, D, F-wave phase shifts and inelasticities for elastic ππ scattering from threshold to 2.0 GeV. As input the S-matrix is required to exhibit poles corresponding to the meson resonance table of the Particle Data Group. As expected, the ππ inelasticity is very strongly related to the opening of the ˉK channel near 1 GeV, and the opening of ρρ(4π) and ωω(6π) channels in the 1.5 GeV region. The predictions of this model are compared to the various elastic ππ→ππ amplitudes, that were obtained from analyses of π⁻ p →π⁻π⁺n data. The role of the various resonances, in particular the glueball candidate f ₀(1500) and the f _J(1710) is investigated. Received: 19 November 1997     

Characterization of a miniature Paul-Straubel trap

Frequency standard applications and ultra-high resolution spectroscopy of a confined single ion require traps of drastically reduced dimensions (about or below 1 mm). These small dimensions increase the sensitivity of the trapping behavior to imperfections in the trap geometry and to patch potentials. For the aim of the metrological laser interrogation of a single Ca⁺ ion, a miniature cylindrical ring trap was built. In order to optimize the laser cooling process and to reach strong binding conditions, the boundaries of the stability diagram and the zones of low confinement as well as the ion motion properties were characterized. Received 14 November 2000 and Received in final form 1st February 2001