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.     

Dipolar and quadrupolar detection using an FT-ICR MS setup at the MPIK Heidelberg

Dipolar and single-phase two-electrode quadrupolar detection schemes have been investigated at a Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) setup built for the KATRIN experiment at the Max-Planck-Institute for Nuclear Physics (MPIK) in Heidelberg. We present first experimental results of ⁷Li^?+? signals from a cylindrical Penning trap configuration for both detection schemes. While the prominent signal of the conventional dipolar detection scheme marks the reduced cyclotron frequency, the main signal for the quadrupolar detection appears at the sum of the reduced cyclotron frequency and the magnetron frequency. For ideal trapping fields, this sum frequency equals the ion cyclotron frequency ?? _c ?=?qB/(2??m). Sidebands due to the combined motions of the cyclotron mode and magnetron mode are observed by quadrupolar detection which allows the determination of the respective combinations of eigenfrequencies.     

RF-coupling and cooling techniques of stored heavy ions

A tandem Penning trap system, the ISOLTRAP, is now used at the on-line mass separator ISOLDE at CERN, Geneva, for accurate mass measurements of short-lived nuclei. The mass of the stored ions is measured by the determination of the cyclotron frequency _c=qB/m in theB=6 T magnetic field of the trap. A new technique has been developed and implemented to allow reliable high-efficiency loading of the trap with radioactive heavy ions.     

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     

Magnetoplastic effect in irradiated NaCl and LiF crystals

The effect of low x-ray irradiation doses (≈10² rad) on the magnetoplastic effect — the detachment of dislocations from paramagnetic centers under the action of an external magnetic field B — in alkali-halide crystals has been investigated. The measurements were performed on LiF crystals and three types of NaCl crystals, differing in impurity content. The dependence of the mean free path l of the dislocations on the rotational frequency ν of a sample in a magnetic field was especially sensitive to low irradiation doses. In unirradiated crystals this dependence is a single-step dependence and is characterized by a critical frequency ν _c ∝B ² above which the magnetoplastic effect is not observed. The frequency ν _c depends only on the type of paramagnetic centers, and not on their density. Even the lowest irradiation dose employed (<100 rad) leads to a sharp restructuring of the dependence l(ν), converting it into a two-step dependence (for edge dislocations) with an additional critical frequency ν _c2, that is insensitive to the irradiation dose, and that corresponds to the appearance of magnetically sensitive stoppers of a new type under irradiation. The initial critical frequency ν _c1, as a rule, also varies with the dose, reflecting the change in state of the impurity complexes (Ca in NaCl and Mg in LiF). Specifically, it is shown for NaCl(Ca) crystals that as the irradiation dose increases, the frequency ν _c1 increases, gradually approaching the value ν _c2, so that by the time the dose is ≈300 rad, the dependence l(ν) once again becomes a single-step dependence, dropping sharply only for ν⩾ν _c2. It is shown that the addition of a small number of Ni atoms to a NaCl crystal makes the Ca complexes radiation resistant, and the critical frequency ν _c1 corresponding to them initially equals ν _c2 for crystals with no Ni. The recombination kinetics of radiation defects in the case in which the samples are irradiated under a tungsten lamp was investigated. A possible physical model of the observed dependences is discussed. Zh. éksp. Teor. Fiz. 111, 615–626 (February 1997)     

Subharmonic excitation of the eigenmodes of charged particles in a Penning trap

When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold behaviour. This phenomenon can be explained with the existence of a damping mechanism affecting the electron cloud; a minimum value of the excitation amplitude is required to overcome the damping. We could theoretically explain the observed phenomenon by numerically calculating the solutions of the damped differential Mathieu equation. This numerical analysis accounts for the fact that for a weak damping of the harmonic system we observed an even-odd-staggering of the the different orders of the subharmonics in the axial excitation spectrum.Received: 22 September 2003, Published online: 2 December 2003PACS: 52.27.Jt Nonneutral plasmas - 82.80.Qx Ion cyclotron resonance mass spectrometry     

A phase-imaging technique for cyclotron-frequency measurements

A novel approach to mass measurements at the 10^?9 level for short-lived nuclides with half-lives well below one second is presented. It is based on the projection of the radial ion motion in a Penning trap onto a position-sensitive detector. Compared with the presently employed time-of-flight ion-cyclotron-resonance technique, the novel approach is 25-times faster and provides a 40-fold gain in resolving power. Moreover, it offers a substantially higher sensitivity since just two ions are sufficient to determine the ion’s cyclotron frequency. Systematic effects specific to the technique that can change the measured cyclotron frequency are considered in detail. It is shown that the main factors that limit the maximal accuracy and resolving power of the technique are collisions of the stored ions with residual gas in the trap, the temporal instability of the trapping voltage, the anharmonicities of the trapping potential and the uncertainty introduced by the conversion of the cyclotron to magnetron motion.     

Mass measurements in the endpoint region of the rp-process at SHIPTRAP

The Penning-trap mass spectrometer SHIPTRAP was designed for precision mass measurements of radionuclides produced in fusion–evaporation reactions. The latest measurement campaign covered heavy nuclei (A>90) related to the astrophysical rapid proton capture process. The masses of 34 neutron-deficient radionuclides have been measured since February 2006 with relative uncertainties between 5×10⁻⁸ and 1×10⁻⁷. Furthermore, the use of an octupolar RF excitation for the time-of-flight ion-cyclotron-resonance technique was investigated and an increase of the resolving power by a factor of ten was observed in agreement with simulations. This will allow to resolve isomeric states with excitation energies of a few 10 keV only.      

Evaporative cooling of hydrogen molecular ions in a Penning trap

Evaporative cooling of singly charged ions in a Penning trap is studied. The ions are created by in-situ electron bombardment of hydrogen molecules and trapped in a cylindrical Penning trap. Cooling of the ions is observed by their axial motion after trapping of a few hundred milliseconds. The ions temperature decreases by a factor of more than 6 in 800 ms, while the bunch density of the coldest ions increases by up to a factor of 10. By studying the time constants of the dependence of ion loss and axial temperature on the magnetic field strength, we exclude the effects of ions loss through the cyclotron motion on the axial ion temperature.     

First absolute mass measurements of short-lived isotopes

Absolute mass measurements of short-lived isotopes have been performed at the on-line mass separator ISOLDE at CERN by determining the cyclotron frequencies of ions confined in a Penning trap. The cyclotron frequencies for^{77,78,85,86,88}Rb and⁸⁸Sr ions could be determined with a resolving power of 3×10⁵ and an accuracy of better than 10⁻⁶, which corresponds to 100 keV for massA=100. The shortest-lived isotope under investigation was⁷⁷Rb with a half-life of 3.7 min. The resonances obtained for the isobars⁸⁸Rb and⁸⁸Sr were clearly resolved.     

Is realization of Majorana neutrino and neutrinoless double beta decay possible in the framework of standard weak interactions?

Usually it is supposed that Majorana neutrino produced in the superposition state χ _L = ν _L + (ν _L ) ^c and then follows the neutrinoless double beta decay. But since the standard weak interactions are chiral invariant then neutrino at production has definite helicity (ν _L and (ν _L ) ^c have opposite spirality). Then these neutrinos are separately produced and their superposition state cannot appear. Thus we see that for unsuitable helicity the neutrinoless double β decay is not possible even if it is supposed that neutrino is a Majorana particle (i.e. there is not a lepton number which is conserved). Also transition of Majorana neutrino ν _L into antineutrino (ν _L ) ^c at their oscillations is forbidden since helicity in vacuum holds. Transition Majora neutrino ν _L into (ν _R ) ^c (i.e., ν _L → (ν _R ) ^c ) at oscillations is unobserved since it is supposed that mass of (ν _R ) ^c is very big. If neutrino is a Dirac particle there can be transition of ν _L neutrino into (sterile) antineutrino $ \bar v_R $ \bar v_R (i.e., ν _L → $ \bar v_R $ \bar v_R ) at neutrino oscillations if there takes place double violation of lepton number. It is necessary also to remark that introducing of a Majorana neutrino implies violation of global and local gauge invariance in the standard weak interactions.     

Spin splitting in HgTe/CdHgTe (013) quantum well heterostructures

The electron transport and cyclotron resonance in a one-sided selectively doped HgTe/CdHgTe (013) heterostructure with a 15-nm quantum well with an inverted band structure have been investigated. The modulation of the Shubnikov-de Haas oscillations has been observed, and the spin splitting in zero magnetic field has been found to be about 30 meV. A large Δm _c/m _c ≃ 0.12 splitting of the cyclotron resonance line has been discovered and shown to be due to both the spin splitting and the strong nonparabolicity of the dispersion relation in the conduction band.     

Resonant Raman scattering and photochromic effects in KI:MnO 4 −

A study is reported of photoinduced bleaching in the resonant Raman (RR) scattering spectra of KI:MnO ₄ ⁻ crystals under laser excitation of the MnO ₄ ⁻ centers in resonance with the ¹ A ₁→¹ T ₂ optical transition. The bleaching effect is found to exist for all RR lines and is studied in detail as a function of time, temperature, and laser excitation power for the ν ₁ line. A reversible and an irreversible process are observed, whose contributions to the total effect depend on temperature. It is established that the decrease in RR intensity is accompanied by a decrease in integrated impurity absorption. The observed photochromic effects are attributed to photoinduced instability of the MnO ₄ ⁻ ions. The results find qualitative interpretation within a three-center model including the following photoelectronic processes: photothermal ionization of the permanganate, electron ejection from the excited state of the impurity center into the conduction band, and electron capture by traps of two types, with subsequent trap reactivation. The intensity distribution in a multiphonon RR scattering spectrum obtained at 5 K is used to find the main electron-phonon interaction constants. The introduction of the permanganate ion is found to excite a local lattice vibration, which is observed both near the exciting line and in combination with the fully symmetric intramolecular vibration of the impurity ion itself. Fiz. Tverd. Tela (St. Petersburg) 39, 1567–1574 (September 1997)     

Electronic detection of a single particle in a coplanar-waveguide Penning trap

We present a detailed model of the electronic detection of a single particle in a coplanar-waveguide Penning trap. The detection signal is the electric current induced upon the trap’s surface by the charged particle’s motion. In contrast to three-dimensional hyperbolic or cylindrical traps, the cyclotron and magnetron motions can be detected, excited or coupled to the axial motion without segmenting any of the trap’s electrodes. We calculate the effective coupling displacement for different electrodes. This determines the detection signal and resistive cooling time constant for each component of the ion’s motion. We discuss the practical implementation of the electronic detection for a single electron and a single proton.     

Beam purification techniques for low energy rare isotope beams from a gas cell

A linear gas stopping cell has been implemented at the NSCL as part of the Low Energy Beam and Ion Trap (LEBIT) facility. The gas stopping cell is used to convert relativistic ions into low energy ions suitable for use in ion trap experiments. A common undesired property of such systems is the production of beam contaminants through charge exchange of gas impurities with the He⁺ ions produced in the stopping process. These contaminants are of particular concern for Penning trap mass spectrometry, where the simultaneous trapping of ions with different masses can cause unwanted shifts in the measured cyclotron frequency of the desired ions. In order to minimize such effects, a multi-stage beam purification system has been implemented at LEBIT.     

Precise - and -factor measurements of Ba+ isotopes

Laser-microwave double and triple resonance experiments were performed on clouds of Ba⁺ ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. Collisions with buffer gas molecules in the trap was used to reduce the lifetime of a long lived metastable state of the ions, in which population trapping might occur, and to cool the ions to the ambient temperature. Loss of ions from the trap by collisions were prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in ¹³⁸Ba⁺ and ¹³⁵Ba⁺ were observed at a full width of about 3 kHz at a transition frequency of 80 GHz. The uncertainty of the line center was . From the magnetic field calibration by the cyclotron resonance of electrons stored in the same trap the g_J-factor for both isotopes could be determined to . From radiofrequency induced transitions of ¹³⁵Ba⁺ the nuclear g-factor could be determined . Both measurements improve earlier results by about one order of magnitude. Received: 9 July 1998 / Accepted: 14 July 1998     

Properties of<Emphasis Type="Italic">B</Emphasis><Subscript>c</Subscript> meson

The mass spectrum ofcb meson is investigated with an effective quark-antiquark potential of the form -α_c/r +Ar ^νwith ν varying from 0.5 to 2.0. TheS andP-wave masses, pseudoscalar decay constant, weak decay partial widths in spectator model and the lifetime ofB _cmeson are computed. The properties calculated here are found to be in good agreement with other theoretical and experimental values at potential index,ν = 1     

The SMILETRAP (Stockholm-Mainz-Ion-LEvitation-TRAP) facility

Described in this paper is an experimental facility which measures atomic masses by using multiply charged ions from an electron beam ion source. The ions are injected into a Penning trap and the cyclotron frequencies measured. A precision of 2×10^–9 has been reached using highly charged carbon, nitrogen, oxygen and neon.