Frequency Rf Field Research Articles

Electron energy distribution functions and power transfer data for radio-frequency discharges in CO2 laser gas mixtures

The electron energy distribution function (EEDF) for an RF discharge in a typical CO2 laser gas mixture was calculated by solving the time-dependent Boltzmann equation. The results were used to evaluate power transfer data to the electron system and subsequently to the different degrees of freedom of the gas mixture. In particular the authors investigated the dependence of the EEDF on the RF field frequency for specific field amplitudes EO/N up to 10-15 V cm2. A comparison has been made with the results based on a quasistationary treatment (low frequency limit) and on the stationary solution of the Boltzmann equation assuming a constant specific field. The latter case models a DC discharge as well as an RF discharge in the high-frequency limit, reading the specific field as an effective value of the RF field.

Electron kinetics in a collision-dominated SiH4 rf plasma including self-consistent rf field strength calculation

The electron kinetics of a collision-dominated rf plasma in silane has been studied by solving the nonstationary electron Boltzmann equation. Ionization and attachment processes and the spatially averaged electron loss to the plasma wall by ambipolar diffusion have been included in the kinetic approach. This makes it possible to calculate, in addition to the time-resolved energy distribution, the self-consistent rf field amplitude which is necessary for the maintenance of the steady-state rf discharge. The impact of the rf field frequency, of the density ratio of negative ions to electrons, and of superelastic (second kind) collisions with excited silane molecules was studied. In particular, large, rf field amplitudes of about 100 V cm−1 Torr−1 result, connected with large modulations of the energy distribution for field frequencies in the megahertz region.

Electron kinetics of collision dominated r.f. bulk plasma in CO: The role of second-kind collisions

Electron energy distribution functions (EEDF) and related properties in the bulk region of the rf CO plasma at the reduced rf field frequency ω/p0=π×107 sec−1 torr−1 have been calculated by solving the time-dependent spatially homogeneous Boltzmann equation in the presence of second-kind collisions and have been interpreted on a microphysical basis. The results show that second-kind collisions (vibrational and electronic) strongly affect the temporal evolution of EEDF, of the mean energy, and of the mean collision frequencies for vibrational and electronic excitation processes, as well as for ionization. In particular, second-kind collisions in the CO rf bulk plasma strongly decrease the modulation of the mean ionization frequency during its periodical alteration in the rf field. Furthermore, the effect of second-kind collisions on an approximate determination of the time-averaged EEDF in the rf bulk plasma using the so-called effective-field appriximation has been estimated.

Resonance effects for different states of a circulating bubble

The influence of an RF field superimposed on the DC bias on the tangential drive requirement of a moving bubble was measured. The bubble was maintained in continuous circular motion in a rotating gradient apparatus. With appropriate amplitude and frequency of RF field, the drive field required to move the bubble could be reduced. A minimum in the drive field occurred at an RF frequency of about 20 MHz. The measurements were performed for bubbles with and without Bloch lines. There was no discernible difference in drive field requirement between S=1 and S=0 bubbles. A harmonic oscillator model for the radial motion combined with the standard model for coercive pressure was used to calculate the expected velocity versus tangential drive relation. The principal features of the experimental results were borne out in the calculations. >

The Impact of Different CO Admixtures on the Electron Kinetics in Collision Dominated RF He/CO Bulk Plasmas

AbstractElectron energy distribution functions and mean collision frequencles for the uniform bulk plasma of established rf discharges in He/CO have been obtained by solving the time dependent Boltzmann equation. The results, which are of importance for plasma processing and laser technology, show that already small CO admixtures to He remarkably changes the periodic behaviour of the energy distribution of the electrons by drastical enhancement of the collisional energy dissipation effectiveness in the mixture. These changes can be interpreted on the basis of a lumped energy dissipation frequency in all electron collisions which is determined by the atomic data of the electron collision processes as well as by the admixture fractions and which drastically increases with increasing CO admixture. The degree of modulation of the energy distribution in different parts of the electron energy space and its population on the time average at higher energies are determined by the relation between the rf field frequency and the mentioned lumped energy dissipation frequency.

M�ssbauer study of the fast magnetization reversal in FeBO3 induced by external RF magnetic fields

The effect of fast magnetization reversal induced by external radio frequency (rf) fields has been studied in FeBO3 using the Mossbauer technique. The rf collapse and sideband effects were investigated as a function of intensity for two rf field frequencies: 62 and 36 MHz. The switching times estimated for magnetization reversal are of the same order of magnitude as in amorphous metals and Fe-Ni alloys. Because of the relatively short switching times the magnetization reversal must be of rotational character.

Attachment and ionization in a self-consistent treatment of the electron kinetics of a collision-dominated rf plasma

This paper deals with the self-consistent determination of the rf field amplitude for sustaining the steady-state collision-dominated weakley ionized plasmas in the bulk of the rf discharge and of the time-resolved behavior of the isotropic part of the distribution function as well as of relevant macroscopic quantities in plasmas whose particle loss is dominantly determined by electron attachment. The strict timeresolved treatment is based on the nonstationary Boltzmann equation of the electrons and its numerical solution including, apart from electron number conservative collision processes, the electron attachment and ionization. The investigations are related to an rf plasma in a model gas and in SF6 and are performed for reduced rf field frequencies around 10 MHz Torr−1 which are of particular interest from the point of application of rf discharges for plasma processing. The numerical results show that a large field amplitude of around 160 V cm−1 Torr−1 is necessary to maintain the discharge and that the isotropic distribution, the relevant collision frequencies for attachment and ionization, and the electron density undergo a large modulation during a period of the rf field.

Production of intense low emittance beams for free electron lasers using electron linear accelerators

The production of intense low emittance beams for free electron laser operation requires new approaches to linear accelerator design. Examples are the use of high gradient single cell resonators instead of conventional multi-cavity structures, the use of magnetic bunching at relatively high energies instead of conventional bunching at low energy, and the use of multiple frequency (harmonically related) rf fields for acceleration instead of single frequency fields. Advantages of the use of multiple frequency rf fields will be discussed, and the results of numerical calculations comparing multiple frequency versus single frequency acceleration will be presented.

Efficient adiabatic fast passage for NMR population inversion in the presence of radiofrequency field inhomogeneity and frequency offsets

Abstract Adiabatic fast passage is a powerful tool for uniformly inverting magnetization in the presence of rf magnetic field inhomogeneity and frequency offsets. Long pulses or large rf powers are necessary for this technique to be effective, however, when the usual linear frequency sweep is used. A sweep of the form ω(t) − ω0 = ω1tan(αω1t), on the other hand, is shown to be an order of magnitude more efficient than the linear sweep. Here ω(t) is the rf field frequency, ω0 is the Larmor frequency, w1 = -γB1 (gyromagnetic ratio times rf field strength), and α is a constant determined by w1, the total sweep time, and the range of the frequency sweep. This tangential frequency sweep can produce substantially better inversion than composite pulses of the same amplitude.

NMR spin-lattice relaxation of 1H in iodine doped trans-polyacetylene

A study of NMR spin-lattice relaxation of 1H in iodine doped polyacetylene vs temperature is presented. It is shown the doped polymer differs from the undoped one essentially by the presence of a new mechanism of relaxation proportional to kT. The theoretical description of our experimental data vs temperature is in complete agreement with the RF field frequency study made by Nechtshein et al. at room temperature.

Parametric Heating by Radio-Frequency near the Lower Hybrid Frequency in the JFT-2 Tokamak

Ion heating efficiencies of the central plasma obtained under various experimental conditions indicated that a nonlinear effect played an important role in the ion heating when the high rf power was irradiated to the plasma. Nonlinearly excited electromagnetic modes as well as the parametric decay spectrum of the electrostatic modes, which were also observed simultaneously, sugegested a further excitation of nonresonant quasi-modes decay instability. It wins shown that the ion heating for \(\omega_{0}/\omega_{\text{1h}}(0){\gtrsim}1.13\) (where ω 0 is frequency of irradiated rf field and ω 1h (0) is the lower hybrid frequency at the center of the plasma column) were well explained by the theoretical model having the empirical nonlinear heating rates resulting from the excitation of nonresonant quasi-modes in one-dimensional WKB approximation.

Modified Hartmann–Hahn double NMR in solids for high resolution at low gyromagnetic ratio: CaF2 and quadrupole interaction in MgF2

Moderately high resolution NMR of rare spins in solids is described, using a modified Hartmann–Hahn double resonance experiment. Resolution is achieved by high power resonant decoupling of abundant spins, and the Hartmann–Hahn condition is achieved by irradiation of the rare spins off resonance, which preserves their chemical shift in the rotating frame. The rare spins are saturated with an additional weak variable frequency rf field. Following this cross-polarization period is a period when strong gated rf is applied off resonance to the abundant spins. This permits time-shared observation of the abundant spin magnetization, which reflects saturation of the rare system during the previous cycle. At the same time it serves to replenish the rare spin magnetization because it is off resonance. Transition between the two modes is adiabatic. This method distorts the rare-spin line shape, but a related model experiment is also described which would not do so. This method is expected to be more useful than that of Pines, Gibby, and Waugh for studies of rare low gyromagnetic ratio species (lower than 13C) of spin 1/2 nuclei. The sensitivity limit is estimated to be in the millimolar range and is expected to be independent of gyromagnetic ratio. In CaF2 the 43Ca gyromagnetic ratio is measured to be 286.545±0.01 Hz/G. In MgF2 the 25Mg quadrupolar interaction is inferred to be e2qQ/h=3.2±0.3 MHz, η=0.36±0.04, with the uncertainty arising from lack of a fourth order theory.

Bloch-Siegert shift in optically oriented199Hg vapour

The Bloch-Siegert shift displayed by a spin 1/2 particle system is measured in a double resonance experiment on the ground state of an optically oriented 199Hg vapour. The displacement of the nuclear magnetic resonance peaks corresponding to the one and three quantum transitions are studied as a function of the radiofrequency field intensity. Similarly, the displacement of the component of the vapour polarization which is modulated at twice the RF field frequency is observed. The experimental results are compared with the existing theoretical approaches to the Bloch-Siegert effect, and a good agreement is found with the semiclassical theory leading to the continued fraction solution.

Nuclear Triple Resonance Tickling: Signal at a Combination Frequency combination frequency

The shape of a NMR signal appearing at a frequency which is a combination of three irradiating rf field frequencies has been determined in an AMX spin system under triple resonance tickling conditions.

Hyperfine Structure of the Ground State ofHe+3by the Ion-Storage Exchange-Collision Technique

The hfs of the ground state of $^{3}\mathrm{He}^{+}$ has been studied using the spin-dependent collision processes between stored $^{3}\mathrm{He}^{+}$ ions and a polarized beam of Cs atoms. All possible hfs transitions have been measured in a magnetic field of about 7.13 G. A consecutive-pulse multiple-resonance scheme was developed to detect the only weakly field-dependent transition $(F=0, {m}_{F}=0)\ensuremath{\leftrightarrow}(F=1, {m}_{F}=0)$ in an almost ideally isolated and pure atomic system. Magnetic-resonance disorientation is observed as a change in the number of ions remaining in the rf quadrupole ion trap after a fixed interaction time with both the resonant rf fields and the polarized atomic beam. For the detection of an ion-number signal, the ion macromotion at ${\overline{\ensuremath{\omega}}}_{z}$ was coherently excited by a homogeneous electric field at ${\overline{\ensuremath{\omega}}}_{z}+\ensuremath{\Omega}$, where $\ensuremath{\Omega}$ is the frequency of the inhomogeneous rf field used for trapping. Linewidths of 10 Hz have been measured for the (0, 0) \ensuremath{\leftrightarrow} (1, 0) hfs transition, when the transition was induced during a time of the order of half the electron-spin orientation time in a weak atomic beam. The value for the zero-magnetic-field hfs splitting is $\ensuremath{\Delta}\ensuremath{\nu}=(8665649867\ifmmode\pm\else\textpm\fi{}10)$ Hz. Rate equations for the populations of the hfs Zeeman levels in the presence of the polarized atomic beam and transitions caused by various rf fields are given. Features of the line shape caused by the consecutive-pulse multiple-resonance scheme are also considered. Several mechanisms which may ultimately limit the precision are discussed. A comparison of the experimental result with current theories of the hfs of hydrogenic systems is presented.

Narrowing of Nuclear Magnetic Resonance Lines in a Double Frequency RF Field

The effect of a strong transverse field of frequency ω 1 and amplitude H 1 on the dipolar line width of the nuclear magnetic resonance signal, has been calculated. The resonance signal is supposed to be the response of a weak transverse r f field varying with frequency ω 2 . By choosing the value of ω 1 such that \(\gamma H_{1}{=}\sqrt{2}(\bar{\omega}-\omega_{1})\) where \barω is the average Larmor frequency of spins with the same gyromagnetic ratios γ, it is shown that in solids for γ H 1 ≫ C s t where C s t is the frequency corresponding to the static dipolar line width in the absence of the strong rf field, the width can be reduced to the order of magnitude C s t 2 /γ H 1 . In the case of liquids with 1/τ c ≫ C s t , where τ c is the correlation time of the molecular fluctuations, the line width is already reduced even with only the weak r f field by a factor τ c C s t compared to that of solids; and to achieve further narrowing the same condition for ω 1 as in solids is required and a still stronger c...

Dynamic Nuclear Polarization of Liquids in Very Weak Fields

The validity of the modified Bloch equations (MBE) for liquids in extremely weak dc magnetic fields and large values of electron spin saturation, using linear rf fields, has been checked for anthracene-negative-ion solutions (ANI). Strictly numerical solutions of the MBE were obtained by use of a computer to show the electron spin saturation as functions of rf field strength and frequency. These functions were strongly nonmonotonic and exceed unity in some cases. Dynamic nuclear polarizations were measured by a low-field transient method in which proton free-precession was observed in a weak field. Conventional epr measurements at 3000 and 18 G, cw dynamic nuclear polarization measurements at 18 G, and the low-field transient dynamic nuclear polarization measurements were all compatible with ${T}_{1}={T}_{2}=T=50$ nsec for the ANI at 29\ifmmode^\circ\else\textdegree\fi{}C. The ratio $k$ of nuclear polarization enhancement to the electron spin saturation was found to be very nearly constant, in agreement with the Solomon two-spin relaxation theory. By use of MBE with $T=50$ nsec and setting $k=\ensuremath{-}162$, the results of the dynamic nuclear polarization measurements were fit to very nearly within known experimental errors despite the wide range of low-field resonant and nonresonant conditions and the strongly nonmonotonic curves. No dynamic polarization of the ANI could be obtained with the rf field parallel to the dc field, in agreement with the MBE. However, a crude-oil-derived free radical with ${T}_{1}>{T}_{2}\ensuremath{\approx}10$ nsec yielded about one-third as large a dynamic nuclear polarization with the rf field parallel to the dc field as perpendicular. It was noticed for a deteriorated ANI sample that the time constant for the establishment of a dynamic nuclear polarization exceeded the proton relaxation time and also varied markedly with the strength of the rf field.

Static Spin Temperature Experiments and the Approach to Thermal Equilibrium in the Rotating Reference Frame

Nuclear magnetic resonance experiments were performed which further verify Redfield's assumption that, for large rf fields ${H}_{1}(\ensuremath{\nu})$, a nuclear spin system is properly described by a spin temperature in a reference frame rotating about the Zeeman field with frequency $\ensuremath{\nu}$. As with similar experiments recently performed by Slichter and Holton, the interpretation of our results does not require any assumption about the spin-lattice relaxation mechanism. The measurements were made on the ${\mathrm{Na}}^{23}$ spins in NaCl and the ${\mathrm{F}}^{19}$ spins in Ca${\mathrm{F}}_{2}$. In both materials the agreement between experiment and theory was very good. From the sodium chloride results it is concluded that quadrupole interactions, caused by strains and imperfections, produce an unobservably small increase in the local field ${H}_{l}$, in the crystals used.Also studied was the rate at which the ${\mathrm{Na}}^{23}$ spin system in NaCl approaches thermal equilibrium in the rotating frame. In these experiments the magnetization ${M}_{z}$ was measured as a function of the duration of a saturating pulse of amplitude $2{H}_{1}(\ensuremath{\nu})$. The measurements were made over a time interval which was much shorter than the spin-lattice relaxation time. Our results provide quantitative verification of a recent calculation by Provotorov, who has shown that when ${H}_{1}\ensuremath{\ll}{H}_{l}$, ${M}_{z}({\ensuremath{\tau}}_{a})$ approaches its equilibrium value (in the rotating frame) at a rate determined by a master equation. The master equation derived by Provotorov is in disagreement with the predictions of elementary perturbation theory except when the frequency of the rf field is equal to the Larmor frequency (or when ${\ensuremath{\tau}}_{a}$ is very short).