Karl E. Lonngren

Synchronization of two Lorenz systems using active control

Abstract Using techniques from active control theory, we demonstrate that a coupled Lorenz system can be synchronized. The synchronization is verified using the Simulink feature in MATLAB.

Sequential synchronization of two Lorenz systems using active control

Abstract Using techniques from active control theory, we demonstrate that a coupled Lorenz system can be synchronized. The application of the control elements is sequentially applied and the ensuing synchronization is displayed.

Soliton experiments in plasmas

The experiments on solitons in plasmas performed during the period 1970 to 1982 are reviewed. Suggestions for future experiments are presented.

ION ACOUSTIC WAVE EXCITATION AND ION SHEATH EVOLUTION.

A series of computer simulations and experiments has been performed to investigate the time evolution of an ion space-charge sheath from a solid electrode in a plasma. A large negative step potential (eΔV ≫ kTe) is applied to the boundary of a uniform plasma and the response computed. A fluid model is used for cold ions, and hot electrons in thermal equilibrium are assumed as a neutralizing background. Both the computer simulations and the experiments show the formation of an ion space-charge sheath in a few ion plasma periods and a rarefying disturbance propagating into the plasma with the ion acoustic speed. For a plane electrode this disturbance extends to the electrode, resembling a rarefaction wave as found in ordinary fluid dynamics. For cylindrical and spherical electrodes this disturbance breaks away from the sheath and propagates as an ion acoustic wave into the plasma. The addition of substantial ion-neutral collisions is found to prevent separation of the wave from the sheath. The results of th...

On the synchronization of a class of electronic circuits that exhibit chaos

Abstract The synchronization of two nonlinear electronic circuits that exhibit chaos is numerically demonstrated using techniques from modern control theory. These circuits have been used to model a “jerk” equation and can either be identical or not identical. The technique is initially described using linear circuits.

Synchronization and Control of Chaotic Systems

Abstract Given a chaotic system and an arbitrarily given reference signal, we design a controller based on the reference signal so that the output of the chaotic system follows the given reference signal asymptotically. Examples of a Duffing system being controlled by a reference signal or being synchronized to another Duffing system are presented.

Experiments on Korteweg–de Vries solitons in a positive ion–negative ion plasma

Experiments on the propagation of ion acoustic solitons that propagate in a positive ion–negative ion plasma are described. The solitons are launched from a solid metal disk to which a small negative step voltage [Δφ≊−2(Te/e) V] is applied. The mechanism for the excitation of the soliton, the identification of the fast and the slow modes in such a plasma, and the observation of a transient sheath are presented.

Transient Plasma Sheath—Discovered by Ion‐Acoustic Waves

For a high negative voltage V0 placed impulsively at the edge of a plasma, a sheath is formed of thickness X = (2eV0)1/2(4πnie2)−1/2 This sheath is observed by extrapolating the position of the leading edge of an ionic sound‐wave pulse back to zero time. The ion number density can be obtained from this sheath.

Oblique collision of modified Korteweg–de Vries ion-acoustic solitons

Two-dimensional propagation and oblique collision of modified Korteweg–de Vries (mKdV) ion-acoustic solitons in a plasma with negative ions have been investigated experimentally. At a critical concentration of negative ions, both compressive and rarefractive mKdV solitons exhibit a resonance interaction at a particular amplitude when the colliding angle is fixed. The amplitude is found to be equal for both compressive and rarefractive solitons. The collided solitons suffer a positive phase shift during the interaction. The new solitons formed during the resonant interaction are found to obey the energy and momentum conservation laws of the mKdV solitons for three-wave interaction.

Soliton propagation, collision, and reflection at a sheath in a positive ion–negative ion plasma

Experiments on the propagation and collision of a Korteweg–deVries soliton in a positive ion–negative ion plasma are described. Both a one‐dimensional overtaking collision and a two‐dimensional resonant collision are examined. Soliton propagation into a steady‐state plasma sheath created by an additional biased metal plate in such a plasma is large enough that the detailed soliton motion in the locally inhomogeneous plasma can be easily studied. A partial reflection and partial transmission of the soliton at a critical density within the sheath is observed and interpreted.