Ion-beam–plasma electromagnetic instabilities

2000 ◽  
Vol 64 (1) ◽  
pp. 75-87 ◽  
Author(s):  
K. GOMBEROFF ◽  
L. GOMBEROFF ◽  
H. F. ASTUDILLO
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Electromagnetic Waves ◽  
Ion Beam ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Beam Density ◽  
Left Hand ◽  
Beam Velocity ◽  
Right Hand

It is well known that ion-beam–plasma interactions can destabilize right- and left-hand polarized electromagnetic waves. Owing to the fact that these instabilities have mostly been studied numerically by solving the hot-plasma dispersion relation, their fluid nature has often gone unnoticed. Choosing the ion background to be the rest frame, it is shown that the right-hand polarized instabilities are the result of a merging of the magnetosonic/electron-cyclotron branch of the dispersion relation with the ion beam. For any given ion-beam density and sufficiently large beam velocity, there are always two right- and two left-hand polarized instabilities leading to forward-propagating electromagnetic waves. It is also shown that all right-hand polarized instabilities are resonant instabilities, satisfying ω−kU+Ωp ≈ 0 around their maximum growth rate (ω and k are the frequency and the wavenumber respectively, U is the beam velocity, and Ωp is the proton gyrofrequency). Likewise, when the two left-hand instabilities are simultaneously present, they are also resonant instabilities satisfying ω ≈ Ωp. The high-frequency right-hand resonant instability (ω [Gt ] Ωp) has a maximum growth rate that depends only on the ratio between the beam density and the total density. The range of the unstable spectrum decreases with increasing beam velocity, leading to highly monochromatic radiation.

scholarly journals Excitation of lower hybrid wave by an ion beam in magnetized plasma

2013 ◽  
Vol 31 (4) ◽  
pp. 747-752 ◽  
Author(s):  
Ved Prakash ◽  
Ruby Gupta ◽  
Suresh C. Sharma ◽  
Vijayshri
Keyword(s):  
Growth Rate ◽  
Ion Beam ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Unstable Wave ◽  
Lower Hybrid ◽  
Hybrid Wave ◽  
Lower Hybrid Wave ◽  
Beam Density

AbstractLower hybrid wave excitation in magnetized plasma by an ion beam via Cerenkov interaction is studied. The lower hybrid modes showed maximum growth rate of the instability when phase velocity of the lower hybrid mode along the magnetic field is comparable to the electron thermal velocity. We have derived the expression for the maximum growth rate and found that the growth rate of the instability increases with beam density. Moreover, the maximum growth rate of the instability scales as the one-third power of the beam density. The real part of the frequency of the unstable wave increases as almost the square root of the beam energy.

Electromagnetic ion-beam instabilities in a cold plasma

1996 ◽  
Vol 55 (1) ◽  
pp. 77-86 ◽  
Author(s):  
G. Gnavi ◽  
L. Gomberoff ◽  
F. T. Gratton ◽  
R. M. O. Galvão
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
External Magnetic Field ◽  
Cold Plasma ◽  
Ion Beam ◽  
Negative Energy ◽  
Left Hand ◽  
Right Hand ◽  
Polarized Waves ◽  
The Stability

We study the stability of the cold-plasma dispersion relation for circularly polarized waves in a plasma composed of an ion background and an ion beam. The presence of the beam introduces a resonant branch into the dispersion relation for right-hand-polarized waves propagating in the direction of the external magnetic field, which, for V>Vφ, has negative energy (here V is the beam velocityVφ is the wave phase velocity). Therefore this branch may give rise to explosive instabilities when the waves experience parametric decays. It is shown graphically that resonant right-hand-polarized and non-resonant left-hand-polarized waves, propagating parallel to the external magnetic field, can be unstable. It is also shown that the instability region can extend to large frequencies and wavenumnbers, and that the instability regions have a band structure. The parametric dependence of instability thresholds and marginal modes is also studied.

A unified picture of the parallel whistler mode instability

1973 ◽  
Vol 9 (2) ◽  
pp. 143-159 ◽  
Author(s):  
Ronald W. Landau ◽  
Sami Cuperman
Keyword(s):  
Growth Rate ◽  
Electromagnetic Waves ◽  
Cyclotron Frequency ◽  
Full Range ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Zero Field ◽  
Mode Instability ◽  
Analytic Expressions ◽  
Rates Of Growth

A parametric investigation of parallel right-hand electromagnetic waves below the electron cyclotron frequency has been carried out; this wave is unstable for anisotropic temperatures if T⊥ <T1. Simple analytic expressions for the maximum growth rate have been obtained for the full range of the parameters β1, _ and A_ ≡ (T⊥/T1)_ -1 as they range from zero to infinity. It is shown that the parameter P ≡ β1_A_(A_+1)2 has an important role: (i) for P ≪1, the results of Kennel & Petschek (1966), for large resonant velocities, hold; (ii) for P ≫ 1, the results of Sudan (1963, 1965) for small resonant velocities are recovered; (iii) for P ≫ 1 and A ≫ 1, the growth rate approaches an upper limit (near the plasma frequency for hot plasmas) identical to the zero field instability of Weibel (1959). For the case P ≫ l and moderate A values (i.e. Sudan's regime), analytic expressions for the rates of growth are calculated without restriction on their magnitude.

Visco-instability of shear viscoelastic collisional dusty plasma systems

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
M. Mahdavi-Gharavi ◽  
K. Hajisharifi ◽  
H. Mehidan
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Dusty Plasma ◽  
Maximum Growth ◽  
Dusty Plasmas ◽  
Maximum Growth Rate ◽  
Linear Perturbation ◽  
Kinetic Regime ◽  
Newtonian Case ◽  
Friction Term

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjee et al.’s work (Banerjee et al., New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.

A note on growth curves of rabbit lines selected on growth rate or litter size

1993 ◽  
Vol 57 (2) ◽  
pp. 332-334 ◽  
Author(s):  
A. Blasco ◽  
E. Gómez
Keyword(s):  
Growth Rate ◽  
Litter Size ◽  
Growth Curves ◽  
Live Weight ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Standard Errors ◽  
Adult Weight ◽  
Weight Growth ◽  
Using Data

Two synthetic lines of rabbits were used in the experiment. Line V, selected on litter size, and line R, selected on growth rate. Ninety-six animals were randomly collected from 48 litters, taking a male and a female each time. Richards and Gompertz growth curves were fitted. Sexual dimorphism appeared in the line V but not in the R. Values for b and k were similar in all curves. Maximum growth rate took place in weeks 7 to 8. A break due to weaning could be observed in weeks 4 to 5. Although there is a remarkable similarity of the values of all the parameters using data from the first 20 weeks only, the higher standard errors on adult weight would make 30 weeks the preferable time to take data for live-weight growth curves.

Reassessment of Maximum Growth Rates for C3 and C4 Crops

1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growing Season ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Crop Growth ◽  
Close Inspection ◽  
Similar Difference ◽  
Photosynthetic Efficiencies

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.

Plasma instabilities driven by pickup ions of ring-beam velocity distributions in the outer heliosheath 

2021 ◽  
Author(s):  
Ameneh Mousavi ◽  
Kaijun Liu ◽  
Sina Sadeghzadeh
Keyword(s):  
Magnetic Field ◽  
Maximum Growth ◽  
Dispersion Analysis ◽  
Maximum Growth Rate ◽  
Injection Velocity ◽  
Plasma Instabilities ◽  
Pickup Ions ◽  
Beam Velocity ◽  
Background Magnetic Field ◽  
Hybrid Simulations

&lt;p&gt;&lt;span&gt;The stability of the pickup ions in the outer heliosheath has been studied by many researchers because of its relevance to the energetic neutral atom (ENA) ribbon observed by the Interstellar Boundary EXplorer. However, previous studies are primarily limited to pickup ions of near &lt;/span&gt;&lt;span&gt;90&amp;#176; &lt;/span&gt;&lt;span&gt;pickup angles, the angle between the pickup ion injection velocity and the background, local interstellar magnetic field. Investigations on pickup ions of smaller pickup angles are still lacking. In this paper, linear kinetic dispersion analysis and hybrid simulations are carried out to examine the plasma instabilities driven by pickup ions of ring-beam velocity distributions at various pickup angles between zero and &lt;/span&gt;&lt;span&gt;90&amp;#176;&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;Parallel propagating waves are studied in the parameter regime where the parallel thermal spread of the pickup ions falls into the Alfv&amp;#233;n cyclotron stability gap. &lt;/span&gt;&lt;span&gt;The linear analysis results and hybrid simulations both show that the fastest growing modes are the right-hand helicity waves propagating in the direction of the background magnetic field, and the maximum growth rate occurs at the pickup angle of &lt;/span&gt;&lt;span&gt;82&amp;#176;&lt;/span&gt;&lt;span&gt;. The simulation results further reveal that the saturation level of the fluctuating magnetic fields for pickup angles below &lt;/span&gt;&lt;span&gt;45&amp;#176; &lt;/span&gt;&lt;span&gt;is higher than that for pickup angles above &lt;/span&gt;&lt;span&gt;45&amp;#176;&lt;/span&gt;&lt;span&gt;. So, the scattering of pickup ions at near zero pickup angles is likely more pronounced than that at near &lt;/span&gt;&lt;span&gt;90&amp;#176; &lt;/span&gt;&lt;span&gt;pickup angles&lt;/span&gt; .&lt;/p&gt;

Interpretation of Experimental Data with Regard to the Activated Sludge Model No.1 and Calibration of the Model for Municipal Wastewater Treatment Plants

1992 ◽  
Vol 25 (6) ◽  
pp. 167-183 ◽  
Author(s):  
H. Siegrist ◽  
M. Tschui
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Activated Sludge ◽  
Municipal Wastewater ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Municipal Wastewater Treatment ◽  
Activated Sludge Model

The wastewater of the municipal treatment plants Zürich-Werdhölzli (350000 population equivalents), Zürich-Glatt (110000), and Wattwil (20000) have been characterized with regard to the activated sludge model Nr.1 of the IAWPRC task group. Zürich-Glatt and Wattwil are partly nitrifying treatment plants and Zürich-Werdhölzli is fully nitrifying. The mixing characteristics of the aeration tanks at Werdhölzli and Glatt were determined with sodium bromide as a tracer. The experimental data were used to calibrate hydrolysis, heterotrophic growth and nitrification. Problems arising by calibrating hydrolysis of the paniculate material and by measuring oxygen consumption of heterotrophic and nitrifying microorganisms are discussed. For hydrolysis the experimental data indicate first-order kinetics. For nitrification a maximum growth rate of 0.40±0.07 d−1, corresponding to an observed growth rate of 0.26±0.04 d−1 was calculated at 10°C. The half velocity constant found for 12 and 20°C was 2 mg NH4-N/l. The calibrated model was verified with experimental dam of me Zürich-Werdhölzli treatment plant during ammonia shock load.

Dietary Protein Requirements of Fishes — A Reassessment

1987 ◽  
Vol 44 (11) ◽  
pp. 1995-2001 ◽  
Author(s):  
Stephen H. Bowen
Keyword(s):  
Growth Rate ◽  
Dietary Protein ◽  
Protein Concentration ◽  
Trophic Ecology ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Intake Rate ◽  
Protein Requirement ◽  
Fish Physiology ◽  
Protein Retention

It is widely believed that fishes require more dietary protein than other vertebrates. Many aspects of fish physiology, nutrition, and trophic ecology have been interpreted within the context of this high protein requirement. Here, fishes are compared with terrestrial homeotherms in terms of (1) protein requirement for maintenance, (2) relative protein concentration in the diet required for maximum growth rate, (3) protein intake rate required for maximum growth rate, (4) efficiency of protein retention in growth, and (5) weight of growth achieved per weight of protein ingested. The two animal groups compared differ only in relative protein concentration in the diet required for maximum growth rate. This difference is explained in terms of homeotherms' greater requirement for energy and does not reflect absolute differences in protein requirement. The remaining measures of protein requirement suggest that fishes and terrestrial homeotherms are remarkably similar in their use of protein as a nutritional resource. Reinterpretation of the role of protein in fish physiology, nutrition, and trophic ecology is perhaps in order.

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