Nonresonant Forces Research Articles

Transient dynamics of a lightly damped, roll-forced pendulum

A roll-forced pendulum is studied as a rudimentary model for a sea-state driven ship crane in this work. Centripetal acceleration measurements were made in a number of non-resonant forcing conditions. In addition to large-amplitude resonant responses, a variety of beating responses were found in the transient mode; this behavior is significant due to the light damping and thus long influence of the transient dynamics. The (transient as well as steady-state) frequency content of the centripetal acceleration spectrum is predicted and compared to experiment using power spectral methods and spectrograms.

Plasma biasing by non-resonant ponderomotive forces of radio-frequency waves

A numerical code that computes stationary radial electric fields E0r induced by ponderomotive forces of radio-frequency waves is developed. The computed value of E0r is typically several hundred volts per centimetre when the wave frequency is 1 % lower or higher than the ion-cyclotron frequency. This value of E0r suggests that the ponderomotively induced electric field would be an effective bias in tokamaks. Numerical data are presented to illustrate the properties of this bias field.

Toroidal currents and radial transport driven by ponderomotive forces of fluctuations in a plasma

Non-resonant ponderomotive force theory is applied to fluctuating electromagnetic fields in a plasma. Bootstrap-type relations between the radial transport velocity and the toroidal current driven by fluctuations are also discussed in the case of non-zero ponderomotive forces proportional to d/dr. A special case of fluctuating fields as measured in the SHEILA heliac is discussed.

Radial plasma transport and toroidal current driven by nonresonant ponderomotive forces

A general form of the time-averaged ponderomotive force produced by radio frequency waves in magnetized plasma configurations is treated. Included in the ponderomotive force are components that result from plasma flow, the dynamo effect, and wave helicity. A detailed description of effects of individual components in the ponderomotive force on radio frequency (RF) driven transport and current is given.

Suppression of chaos by nonresonant parametric perturbations.

It is shown analytically and numerically that the suppression of chaos may be effectively achieved by applying a high-frequency parametric force to a chaotic dynamical system. Such a periodic nonresonant force may decrease or even completely eliminate chaos. Taking the Duffing oscillator as a concrete but rather general example, an analytical approach is elaborated to demonstrate how such a suppression of chaos may be understood in the framework of the effective ``averaged'' nonlinear equation for a slowly varying component of the oscillation amplitude. As follows from our numerical simulations, the suppression of chaos may be observed not only at large amplitudes of the parametric force but also at smaller amplitudes, showing a decay of the leading Lyapunov exponent within certain amplitude-frequency ``windows.''

Applications of non-resonant RF forces for the improvement of tokamak reactor performance

The application of radiofrequency (RF) forces to a tokamak divertor plasma for the improvement of its relevance to reactors is proposed and studied. An RF field is applied to the divertor region of a tokamak by use of wave guide launchers in a way that is suitable for a reactor environment. Since the ponderomotive force is dependent on the charge to mass ratio of the ions, various useful applications are considered. They cover some of the key issues in recent research towards the development of nuclear fusion: reduction of the heat load on the divertor plate, improvement of the tritium inventory, impurity control and helium ash removal

Nonresonant current drive and helicity injection by radio-frequency waves

Current drive via nonresonant interaction between radio-frequency (rf) waves and plasma is studied. The averaged force of rf waves acting on each species of a plasma can be divided into a resonant force and a nonresonant one. A part of the nonresonant force cannot be expressed by a gradient of a scalar potential and remains after integrating along the direction of the force. This force mainly acts as an internal force among plasma species and the net momentum input from the wave to the plasma is usually small. This process is not included in the conventional current drive schemes but is associated with the rf wave helicity injection. Quantitative analysis using a one-dimensional kinetic wave code is applied to waves in the ion cyclotron range of frequencies and low-frequency Alfvén waves in a large tokamak. The driven current is estimated taking account of the effect of the toroidally trapped particles. The spatial profile of the forces acting on electrons and ions as well as the driven current are obtained. The parameter dependence of the current drive efficiency on the wave number, the plasma density, the temperature, and the toroidal magnetic field is compared with the estimate based on a local analysis.

Neoclassical transport induced by ICRF in the collisional regime

From the gyrokinetic equations, a quasilinear equation can be derived with RF effects included in the quasilinear operator. From this, generalized moment equations can be deduced in the guiding center approximation. Of particular interest is the parallel momentum equation which drives the neoclassical transport. The parallel RF forces which can be due to nonresonant or resonant ponderomotive forces are quite different between electrons and ions so that an electrostatic electric field is established. This electric field can influence transport near the plasma edge. We estimate the neoclassical particle and energy fluxes in the Pfirsch-Schlüter regime appropriate for the edge region. Since RF can generate asymmetric momentum and heat sources, it changes the transport in RF heated plasmas and also offers the possibility of externally controlling the density and confinement properties of a tokamak plasma. These effects are discussed in terms of antenna near fields and power requirements. Effects on limiter and divertor discharges will be discussed.

Resonant tool driving system with gap

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The acceleration of minor ion species in the solar wind

This paper provides a comprehensive analysis of the dynamics of the flow of minor ion species in the solar wind under the combined influences of gravity, Coulomb friction (with protons), rotational forces (arising from the Sun's rotation and the interplanetary spiral magnetic field) and wave forces (induced in the minor ion flow by Alfven waves propagating in the solar wind). It is assumed that the solar wind can be considered as a proton-electron plasma which is, to a first approximation, unaffected by the presence of minor ions. In the dense hot region near the Sun Coulomb friction accelerates minor ions outwards against the gravitational force, part of which is cancelled by the charge-separation electric field. Once the initial acceleration has been achieved, wave and rotational forces assist Coulomb friction in further increasing the minor ion speed so that it becomes comparable with, or perhaps even exceeds, the solar wind speed. A characteristic feature of the non-resonant wave force is that it tends to bring the minor ion flow into an equilibrium where the radial speed matches the Alfven speed relative to the solar wind speed, whereas Coulomb friction and rotational forces tend to bring the flow into an equilibrium where the radial speed of the minor ions equals the solar wind speed. Therefore, provided that there is sufficient wave energy and Coulomb friction is weak, the minor ion speed can be ‘trapped’ between these two speeds. This inteststing result is in qualitative agreement with observational findings to the effect that the differential flow speed between helium ions and protons is controlled by the ratio of the solar wind expansion time to the ion-proton collision time. If the thermal speeds of the protons and minor ions are small compared to the Alfven speed, two stable equilibrium speeds can exist because the rapid decrease in the Coulomb cross-section with increasing differential flow speed allows the non-resonant wave force to balance Coulomb friction at more than one ion speed. However, it must be emphasized that resonant wave acceleration and/or strong ion partial pressure gradients are required to achieve radial speeds of minor ions in excess of the proton speed, since, as is shown in Section 4, the non-resonant wave acceleration on protons and minor ions are identical when their radial speeds are the same, with the result that, in the solar wind, non-resonant wave acceleration tends (asymptotically) to equalize minor ion and proton speeds.

Forced oceanic waves

This paper concerns the linear response of the ocean to forcing at a specified frequency and wave number in the absence of mean currents. It discusses the details of the forcing function, the general properties of the equations of motion, and possible simplifications of these equations. Two representations for the oceanic response to forcing are described in detail. One solution is in terms of the normal modes of the ocean. The vertical structure of these modes corresponds to that of the barotropic and baroclinic modes; their latitudinal structure corresponds to that of inertia‐gravity and Rossby waves. These waves are eigenfunctions of Laplace's tidal equations (LTE) with the frequency as eigenvalue. The description in terms of vertically standing modes is particularly useful if the forcing is nonlocal, because only these modes can propagate into undisturbed regions. The principal result is that it is extremely difficult for baroclinic (but not barotropic) disturbances to propagate horizontally away from a forced region. Instabilities of the Gulf Stream excite disturbances that are confined to the immediate neighborhood of the current; disturbances due to instabilities of equatorial currents do not propagate far latitudinally. A second representation of the oceanic response to forcing is in terms of vertically propagating, or vertically trapped, latitudinal modes. These modes are eigenfunctions of LTE with the equivalent depth h (not the frequency) as eigenvalue. Both positive and negative eigenvalues h are necessary for completeness. The modes with h > 0 consist of an infinite set of inertia‐gravity waves and a finite set of Rossby waves which either propagate vertically or form vertically standing modes. The latitudinally gravest modes are equatorially trapped and have been observed in the Atlantic and Pacific oceans. The modes with h < 0 are necessary to describe the oceanic response to nonresonant forcing. In the vertical this response attenuates with increasing distance from the forcing region. Because of the shallowness of the ocean the large eastward traveling atmospheric cyclones in mid‐latitudes and high latitudes force a response down to the ocean floor. Interaction with the bottom topography will result in smaller‐scale disturbances and will affect the frequency spectrum of the response when bottom‐trapped waves are excited.