The Spitzer resistivity (or plasma resistivity), also called 'Spitzer-Harm resistivity', is an expression describing the electrical resistance in a plasma, which was first formulated by Lyman Spitzer in 1950. [1] [2] The Spitzer resistivity of a plasma decreases in proportion to the electron temperature as .
The inverse of the Spitzer resistivity is known as the Spitzer conductivity.
The Spitzer resistivity is a classical model of electrical resistivity based upon electron-ion collisions and it is commonly used in plasma physics. [3] [4] [5] [6] [7] The Spitzer resistivity (in units of ohm-meter) is given by:
where is the ionization of nuclei, is the electron charge, is the electron mass, is the Coulomb logarithm, is the electric permittivity of free space, is the Boltzmann constant, and is the electron temperature (in Kelvin).
One way to convert the of a plasma column to its resistance is to multiply by the length of the column and divide by its area.
In CGS units, the expression is given by:
This formulation assumes a Maxwellian distribution, and the prediction is more accurately determined by [5]
where the factor and the classical approximation (i.e. not including neoclassical effects) of the dependence is:
In the presence of a strong magnetic field (the collision rate is small compared to the gyrofrequency), there are two resistivities corresponding to the current perpendicular and parallel to the magnetic field. The transverse Spitzer resistivity is given by , where the rotation keeps the distribution Maxwellian, effectively removing the factor of .
The parallel current is equivalent to the unmagnetized case, .
Measurements in laboratory experiments and computer simulations have shown that under certain conditions, the resistivity of a plasma tends to be much higher than the Spitzer resistivity. [8] [9] [10] This effect is sometimes known as anomalous resistivity or neoclassical resistivity. [11] It has been observed in space and effects of anomalous resistivity have been postulated to be associated with particle acceleration during magnetic reconnection. [12] [13] [14] There are various theories and models that attempt to describe anomalous resistivity and they are frequently compared to the Spitzer resistivity. [9] [15] [16] [17]
A corona is the outermost layer of a star's atmosphere. It is a hot but relatively dim region of plasma populated by intermittent coronal structures known as solar prominences or filaments.
The Hall effect is the production of a potential difference across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879.
In physics and engineering, magnetohydrodynamics is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in multiple fields including space physics, geophysics, astrophysics, and engineering.
The quantum Hall effect is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values
In particle physics, bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.
Electrical resistivity is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.
Johnson–Nyquist noise is the electronic noise generated by the thermal agitation of the charge carriers inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments. Thermal noise is proportional to absolute temperature, so some sensitive electronic equipment such as radio telescope receivers are cooled to cryogenic temperatures to improve their signal-to-noise ratio. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.
Magnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave speed, which is the fundamental speed for mechanical information flow in a magnetized plasma.
The diffusion of plasma across a magnetic field was conjectured to follow the Bohm diffusion scaling as indicated from the early plasma experiments of very lossy machines. This predicted that the rate of diffusion was linear with temperature and inversely linear with the strength of the confining magnetic field.
In physics, the Einstein relation is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their works on Brownian motion. The more general form of the equation in the classical case is
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by:
In quantum electrodynamics, Bhabha scattering is the electron-positron scattering process:
A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is the ratio of the magnetic moment of a particle to that expected of a classical particle of the same charge and angular momentum. In nuclear physics, the nuclear magneton replaces the classically expected magnetic moment in the definition. The two definitions coincide for the proton.
In plasma physics, the Lundquist number is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfvén velocity is the typical velocity scale of the system, and is given by
Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number. Magnetohydrodynamics (MHD) deals with what is a quasi-neutral fluid with very high conductivity. The fluid approximation implies that the focus is on macro length-and-time scales which are much larger than the collision length and collision time respectively.
In atomic physics, a Zeeman slower is a scientific instrument that is commonly used in atomic physics to slow and cool a beam of hot atoms to speeds of several meters per second and temperatures below a kelvin. The gas-phase atoms used in atomic physics are often generated in an oven by heating a solid or liquid atomic sample to temperatures where the vapor pressure is high enough that a substantial number of atoms are in the gas phase. These atoms effuse out of a hole in the oven with average speeds on the order of hundreds of m/s and large velocity distributions. The Zeeman slower is attached close to where the hot atoms exit the oven and are used to slow them to less than 10 m/s (slowing) with a very small velocity spread (cooling).
In thermal quantum field theory, the Matsubara frequency summation is a technique used to simplify calculations involving Euclidean path integrals.
A sawtooth is a relaxation that is commonly observed in the core of tokamak plasmas, first reported in 1974. The relaxations occur quasi-periodically and cause a sudden drop in the temperature and density in the center of the plasma. A soft-xray pinhole camera pointed toward the plasma core during sawtooth activity will produce a sawtooth-like signal. Sawteeth effectively limit the amplitude of the central current density. The Kadomtsev model of sawteeth is a classic example of magnetic reconnection. Other repeated relaxation oscillations occurring in tokamaks include the edge localized mode (ELM) which effectively limits the pressure gradient at the plasma edge and the fishbone instability which effectively limits the density and pressure of fast particles.
James F. Drake is an American theoretical physicist who specializes in plasma physics. He is known for his studies on plasma instabilities and magnetic reconnection for which he was awarded the 2010 James Clerk Maxwell Prize for Plasma Physics by the American Physical Society.
Non-linear inverse Compton scattering (NICS), also known as non-linear Compton scattering and multiphoton Compton scattering, is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon during the interaction with a charged particle, in many cases an electron. This process is an inverted variant of Compton scattering since, contrary to it, the charged particle transfers its energy to the outgoing high-energy photon instead of receiving energy from an incoming high-energy photon. Furthermore, differently from Compton scattering, this process is explicitly non-linear because the conditions for multiphoton absorption by the charged particle are reached in the presence of a very intense electromagnetic field, for example, the one produced by high-intensity lasers.
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