scholarly journals Measurement of nonlinear frequency shift coefficient in spin-torque oscillators based on MgO tunnel junctions

2009 ◽  
Vol 95 (2) ◽  
pp. 022507 ◽  
Author(s):  
Kiwamu Kudo ◽  
Tazumi Nagasawa ◽  
Rie Sato ◽  
Koichi Mizushima
Keyword(s):  
Frequency Shift ◽  
Tunnel Junctions ◽  
Spin Torque ◽  
Nonlinear Frequency ◽  
Shift Coefficient ◽  
Nonlinear Frequency Shift ◽  
Spin Torque Oscillators

Soliton formation in magnetized Vlasov plasmas

1979 ◽  
Vol 22 (1) ◽  
pp. 121-147 ◽  
Author(s):  
J. G. Turner ◽  
T. J. M. Boyd
Keyword(s):  
Perturbation Theory ◽  
Schrödinger Equation ◽  
Frequency Shift ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Frequency ◽  
Shift Coefficient ◽  
Reductive Perturbation ◽  
Nonlinear Frequency Shift

Soliton formation at the upper hybrid frequency has been discussed recently on the basis of warm two-fluid theory. In this paper we report the results of a reductive perturbation theory analysis of the Vlasov equation describing the nonlinear modulation of electrostatic waves in a warm magnetized plasma. This approach allows a treatment of soliton formation with scale lengths of the order of, or less than, the electron Larmor radius rL for both upper hybrid and Bernstein waves. A three-dimensional generalized nonlinear Schrödinger equation has been found. Contributions to the nonlinear frequency shift derive from three distinct processes. One contribution describes the generation of the second harmonic governed by (ω + ω) → 2w where ω is the frequency of the electrostatic carrier; a second arises from the self-interaction between the high-frequency waves (ω + ω → ω + ω) while the third contribution describes the nonlinear coupling between the carrier and the slow background plasma motion.Propagation orthogonal to the magnetic field is studied and leads to a simplified nonlinear Schrodinger equation with cubic nonlinearity, predicting soliton formation at the upper hybrid and cyclotron harmonic frequencies. Expressions for the nonlinear frequency shift coefficient are presented for the upper hybrid and Bernstein modes in the low temperature limit and the relative strengths of the three competing nonlinear processes are compared. For krL ≥ 1·0, numerical analysis shows the dominant nonlinearity to be that arising from the nonlinear wave-particle interaction. The stability of the soliton solution is determined by the relative signs of the dispersion and the nonlinear frequency shift coefficient. Some properties of upper hybrid and Bernstein solitons are examined. In particular the variation of the normalized dispersion and nonlinear frequency shift coefficient with the basic plasma parameters (krL)2 and (ωpe/Ω, is presented, where (ope, fi are the electron plasma frequency and electron gyrofrequency respectively. Regions of instability are identified for both upper hybrid and Bernstein modes. The connection between reductive perturbation theory and previous warm fluid theories is also established.

Notch Nonlinear Frequency Shift in AlGaAs Bragg Grating Waveguides

2011 ◽  
Author(s):  
P. Tannouri ◽  
M. J. Strain ◽  
M. Clerici ◽  
M. Peccianti ◽  
A. Pasquazi ◽  
...  
Keyword(s):  
Frequency Shift ◽  
Bragg Grating ◽  
Nonlinear Frequency ◽  
Nonlinear Frequency Shift

scholarly journals Auto-oscillation and narrow spectral lines in spin-torque oscillators based on MgO magnetic tunnel junctions

2009 ◽  
Vol 106 (10) ◽  
pp. 103921 ◽  
Author(s):  
T. Devolder ◽  
L. Bianchini ◽  
Joo-Von Kim ◽  
P. Crozat ◽  
C. Chappert ◽  
...  
Keyword(s):  
Tunnel Junctions ◽  
Magnetic Tunnel Junctions ◽  
Spectral Lines ◽  
Spin Torque ◽  
Spin Torque Oscillators

Nonlinear frequency shift of finite-amplitude electrostatic surface waves

1989 ◽  
Vol 41 (2) ◽  
pp. 239-242 ◽  
Author(s):  
L. Stenflo ◽  
M. Y. Yu
Keyword(s):  
Frequency Shift ◽  
Surface Waves ◽  
Spatial Dependence ◽  
Wave Amplitude ◽  
Finite Amplitude ◽  
Nonlinear Frequency ◽  
Unmagnetized Plasma ◽  
Nonlinear Frequency Shift

The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov (1987b), who assumed a linear exponential attenuation behaviour.

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