On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure

Theory and applications of the Vlasov equation

Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and applications of the Vlasov equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of scientific results involving the Vlasov equation. In this editorial, after some introductory notes, a brief account is given of the main points addressed in these papers and of the perspectives they open.Comment: Editoria

Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence

Stability properties and mode signature for equilibria of a model of electron temperature gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving the infinite families of Casimir invariants, associated with the noncanonical Poisson bracket of the model, a sufficient condition for stability is obtained by means of the Energy-Casimir method. Mode signature is then investigated for linear motions about homogeneous equilibria. Depending on the sign of the equilibrium "translated" pressure gradient, stable equilibria can either be energy stable, i.e.\ possess definite linearized perturbation energy (Hamiltonian), or spectrally stable with the existence of negative energy modes (NEMs). The ETG instability is then shown to arise through a Kre\u{\i}n-type bifurcation, due to the merging of a positive and a negative energy mode, corresponding to two modified drift waves admitted by the system. The Hamiltonian of the linearized system is then explicitly transformed into normal form, which unambiguously defines mode signature. In particular, the fast mode turns out to always be a positive energy mode (PEM), whereas the energy of the slow mode can have either positive or negative sign

Smoking-related cancer in military veterans: retrospective cohort study of 57,000 veterans and 173,000 matched non-veterans

Background: Serving military personnel are more likely to smoke, and to smoke more heavily, than civilians. The aim of our study was to examine whether veterans have an increased risk of a range of smoking-related cancers compared with non-veterans, using a large, national cohort of veterans. Methods: We conducted a retrospective cohort study of 57,000 veterans resident in Scotland and 173,000 age, sex and area of residence matched civilians. We used Cox proportional hazard models to compare the risk of any cancer, lung cancer and other smoking-related cancers overall, by sex and by birth cohort, adjusting for the potential confounding effect of socioeconomic deprivation. Results: Over a mean of 29 years follow-up, 445 (0.79 %) veterans developed lung cancer compared with 1106 (0.64 %) non-veterans (adjusted hazard ratio 1.16, 95 % confidence intervals 1.04–1.30, p = 0.008). Other smoking-related cancers occurred in 737 (1.31 %) veterans compared with 1883 (1.09 %) non-veterans (adjusted hazard ratio 1.18, 95 % confidence intervals 1.08–1.29, p < 0.001). A significantly increased risk was observed among veterans born 1950–1954 for lung cancer and 1945–1954 for other smoking-related cancers. The risk of lung cancer was decreased among veterans born 1960 onwards. In comparison, there was no difference in the risk of any cancer overall (adjusted hazard ratio 0.98, 95 % confidence intervals 0.94–1.01, p = 0.171), whilst younger veterans were at reduced risk of any cancer (adjusted hazard ratio 0.88, 95 % confidence intervals 0.81–0.97, p = 0.006). Conclusions: Military veterans living in Scotland who were born before 1955 are at increased risk of smoking-related cancer compared with non-veterans, but younger veterans are not. The differences may reflect changing patterns of smoking behaviour over time in military personnel which may, in turn, be linked to developments in military health promotion policy and a changing military operational environment, as well as to wider societal factors

Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.Comment: 11 pages, 10 figure