Edited by : M. A. Razzak, Graduate Student, Takamura Lab, Graduate School of Engineering (Nagoya University)


Ballooning instability

A local instability which can develop in the TOKAMAK when the plasma pressure exceeds a critical value; it therefore constrains the maximum beta that can be achieved. It is analogous to the unstable bulge which develops on an over-inflated pneumatic inner tube. See resistive ballooning mode.


Ballooning Mode

A plasma mode, which is localized in regions of unfavorable magnetic field curvature (also known as "bad curvature") that becomes unstable (grows in amplitude) when the force due to plasma pressure gradients is greater than the mean magnetic pressure force.


Banana Orbit

In a toroidal geometry, the ‘fast’ spiraling of a charged particle around a magnetic field line is accompanied by a ‘slow’ drift motion of the particle’s center around the spiral. When projected onto the poloidal plane of a toroidally confined plasma, the drift orbit has the shape of a banana. These orbits are responsible for neo-classical diffusion and for bootstrap current. Also see trapping.



As viewed from the Earth, the heliographic latitude of the center of the solar disk. The center of the solar disk usually does not coincide with the heliographic equator, due to a tilt of the solar axis with respect to the ecliptic. (See Bo under solar coordinates.)


Bartels' rotation number

The serial number assigned to 27-day rotation periods of solar and geophysical parameters. Rotation 1 in this sequence was assigned arbitrarily by Bartels to begin in January 1833, and the count has continued by 27-day intervals to the present. (For example, rotation 2000 began on 12 November 1979, rotation 2030 on 30 January 1982.) The 27-day period was selected empirically from the observed recurrence of geomagnetic activity attributed to co-rotating features on the Sun. The Sun has an average rotation period (as seen from the Earth) of 27.27 days; therefore, solar longitude slowly drifts with respect to the Bartels rate. Compare Carrington longitude.


Baseball Coils

Coils (copper or super conducting) that carry electrical current for producing magnetic fields that are shaped like the seams of a baseball, also known as yin-yang coils.


Beam-Beam Reaction

Fusion reaction that occurs in neutral beam heated plasmas from the collision of two fast ions originating in the neutral beams injected into the plasma for heating purposes. Distinguished from beam-plasma, beam-wall, and thermonuclear (plasma-plasma) reactions.


Beam-Plasma reaction

Fusion reaction that occurs in neutral-beam heated plasmas from the collision of a fast beam ion with a thermal plasma ion.


Beam-Wall reaction

Fusion reaction that occurs in neutral beam heated plasmas from the collision of a fast beam ion with an ion embedded in the plasma vacuum wall.


Bernstein Mode

Type of plasma mode that propagates perpendicular to the equilibrium magnetic field in a plasma. Bernstein waves, named after the plasma physicist, Ira Bernstein, have their electric field nearly parallel to the wave propagation vector and their frequency between harmonics of the electron cyclotron frequency.



(1)  b = p/(B2/2mo).  The ratio of plasma gas pressure (p) to magnetic field pressure (B2/2mo) in a TOKAMAK.  p is the gas pressure in Pascals (Newton/meter2), B is the magnetic field strength in Tesla, and mo = 4p x 10-7 Henry/meter.

(2)  Ratio of plasma pressure to magnetic field pressure. One of the figures of merit for magnetic confinement: the magnitude of the magnetic field pressure is determined by the expenditure on the field coils, etc., that generate it; since fusion reactivity increases with plasma pressure, a high value of beta is an indicator of good performance. The highest value of beta achieved in a large TOKAMAK is about 13%, though much higher values are theoretically possible at low aspect ratio and have been achieved on START.


Beta limit

(1)  Maximum beta attainable, usually due to a deterioration in the confinement. The Troyon beta limit, which states that beta (in percent) cannot exceed g.I / a.B is often quoted. Here, g is the so-called Troyon coefficient, and has an value of around 3.5 for conventional TOKAMAKs. (I is the plasma current in MegaAmps, a is the minor radius in metres, and B is the toroidal field in Tesla.) The normalised beta is given by beta.a.B / I, and (when quoted in percent) cannot exceed g.

(2)  Also known as the Troyon Limit in a tokamak, the beta limit is the maximum achievable ratio (beta, or beta value) of plasma pressure to magnetic pressure for a given plasma to remain stable. In a tokamak, if the beta value is too high, ballooning modes become unstable and lead to a loss of plasma confinement.


Beta particle

An electron emitted from the nucleus of a radioactive element and denoted by the Greek letter, beta (b).


Beta poloidal

See poloidal beta.


Beta, beta value

Ratio of plasma kinetic pressure to magnetic field pressure. Beta is usually measured relative to the total, local magnetic field but in some cases can be measured relative to components of the total field, such as the poloidal field in tokamaks.


Binding energy

In nuclear reactions, the energy associated with removing protons and/or neutrons from the nucleus; in standard chemistry, it is the energy associated with electronic bond making and breaking.


Bipolar magnetic region

A region of the solar photosphere containing at least two areas of enhanced magnetic fields of opposing polarity.


Birkeland currents

Electric currents linking the Earth's ionosphere with more distant regions, flowing along magnetic field lines. Named for Kristian Birkeland, a pioneer of auroral research who first proposed such currents around 1900, these currents are often associated with the polar aurora.


Blackbody temperature

The temperature of an object if it is reradiating all the thermal energy that has been added to it; if an object is not a blackbody radiator, it will not reradiate all the excess heat and the leftover will go toward increasing its temperature.


(1) The physical system surrounding the hot plasma that provides shielding and absorbs fast neutrons, converts the energy into heat, and produces tritium.  Blanket technology for the practical application of harnessing fusion energy is still under development. The ultimate design may include a liquid metal such as molten lithium, which produces tritium when it captures neutrons.

(2)  In a fusion power plant using deuterium-tritium fuel, the system surrounding the plasma vessel used to slow down the neutrons produced, so that the heat released can be used for electricity generation. In many designs, the blanket is also used to synthesise tritium (from the neutrons and a lithium compound) to use as fuel. See breeder.


Bohm diffusion

A rapid loss of plasma particles across magnetic field lines caused by plasma microinstabilities that scales inversely with the magnetic field strength, unlike classical diffusion that scales inversely as the square of the magnetic field strength. Named after the plasma physicist David Bohm who first proposed such scaling.


Bohm transport

Bohm transport is the anomalous diffusion associated with long wavelength plasma fluctuations and has the consequence that confinement times increase linearly with magnetic field. In gyro-Bohm transport, fluctuations have a shorter scale length, comparable with the ion gyro-radius, and consequently the confinement time increases quadratically with magnetic field. Gyro-Bohm transport is therefore more optimistic than Bohm for large scale devices like ITER.


Bohr-Einstein Radiation Formula

The internal electronic energy changes of an atom are connected to the frequency of the corresponding emitted radiation by the formula ε=h.ν, with h the Planck constant. Usually, this equation is assumed to determine uniquely the resulting intensity of the radiation. However, there is theoretical and observational evidence that this assumption is only valid if the broadening of the spectral line due to plasma field fluctuations (Stark broadening) is small compared to the natural broadening. In general, one has to assume a relationship in the form εrad=(1+Δνm,nD/Ai,k).h.ν , where Δνm,nD is the dynamical Stark Broadening due to the plasma field fluctuations and Am,n the Atomic Decay Probability (natural broadening). This could for instance resolve the discrepancy if one wants to explain the radiative energy output of the present day sun solely through the gravitational contraction of an initial gas cloud (see


Boltzmann Distribution

Statistical Physics proves that in thermodynamic equilibrium (i.e. in a collisionally determined closed system) the volume density of particles decreases exponentially with increasing energy,i.e. f(ε)= exp(-ε/ε0) .


The energy distribution of electrons within an atom is generally assumed to behave in this way.
However, in most practical cases collisions are quite insignificant compared to radiative processes which are determined by the lifetime of the individual atomic levels. As a consequence, the distribution function has very little to do with a Boltzmann- distribution (see for instance ). (see also Maxwell Distribution, Saha- Equation, LTE).


Boltzmann Equation

As a generalized form of the Continuity Equation, the Boltzmann equation constitutes an exact description for the density of a plasma constituent both in real and velocity space. It can be written as

∂/∂t(n(r,v,t)) +v.gradr(n(r,v,t)) +F/M.gradv(n(r,v,t)) = qIon(r,v,t) +lRec(r,v,t) +C(r,v,t) .


The left-hand side of the equation describes the production and loss rates for the density distribution function n(r,v,t) due to convection (transport) in geometrical and velocity space (where F contains all external forces on the particle with mass M, i.e. electric, magnetic and gravitational forces), whereas the right-hand side contains the local production and loss rates due to ionization (qIon), recombination (lRec) and velocity changing collisions (C).


The steady-state (time independent) equation for is given by setting ∂/∂t(n(r,v,t))=0. The ionization and recombination terms are usually neglected in standard treatments. However, they are vitally important as they are responsible for the inhomogeneities of the plasma density and affect therefore the velocity distribution function through the convection terms in the equation (see link below). Also, one should note that the usual formulation in terms of the normalized distribution function f(r,v,t)= n(r,v,t)/N(r,t) (with N(r,t) = ∫d3v n(r,v,t) ) is in general not sufficient because of the dependence of N(r,t) on r. For the one-dimensional case, the Boltzmann equation can be written as a first order linear differential equation in either the spatial or velocity variable. Formal solution yields a non-linear integral equation which can then be solved numerically. (see for an application to ion diffusion in the earth's ionosphere).


Bootstrap current

(1)  Currents driven in toroidal devices by neo-classical processes (see entry). They may amount to a substantial fraction of the net current in a tokamak reactor, thus lengthening the pulse time or decreasing the power needed for current drive.

(2)  Theory predicted in 1970 that a toroidal electric current will flow in a TOKAMAK which is fuelled by energy and particle sources that replace diffusive losses. This diffusion driven bootstrap current, which is proportional to beta and flows even in the absence of an applied voltage, could be used to provide the confining magnetic field: hence the concept of a bootstrap TOKAMAK, which has no toroidal voltage. A bootstrap current consistent with theory was observed many years later on JET and TFTR; it now plays a role in design of experiments and power plants (especially advanced TOKAMAKs).


Bounce Frequency

The average frequency of oscillation of a particle trapped in a magnetic mirror as it bounces back and forth between its "turning points" in regions of high magnetic field. (See also trapped particle, turning points, banana orbit).


Bow shock

(1)  A collisional shock wave in front of the magnetosphere arising from the interaction of the supersonic solar wind with earth's magnetic field.

(2)  A collisionless shock wave in front of a planetary magnetosphere; the place where the supersonic flow of the solar wind is slowed to subsonic speed by the planetary magnetic field.

(3)  A sharp front formed in the solar wind ahead of the magnetosphere, marked with a sudden slowing-down of the flow near Earth. It is quite similar to the shock forming ahead of the wing of a supersonic airplane. After passing near Earth, the slowed-down flow gains speed again, to the same value as the surrounding solar wind.



The condition in which the fusion power produced by the plasma equals the heating power put into the plasma. For a fusion power reactor to be economically useful, a burning plasma must produce much more fusion power than it consumes, thereby significantly exceeding the breakeven point.


Breakeven (commercial, engineering, scientific, and extrapolated)

(1)  Commercial Breakeven is when sufficient fusion power can be converted into electric power to cover the costs of the fusion power plant at economically competitive rates.

(2)   Engineering Breakeven is when sufficient electrical power can be generated from the fusion power output to supply power for the plasma reactor plus a net surplus without the economic considerations.

(3)  Scientific Breakeven is when the fusion power is equal to input power; i.e. Q=1. (See also Lawson Criterion).

(4)  Extrapolated Breakeven is when scientific breakeven is projected for actual reactor fuel (e.g., deuterium and tritium) from experimental results using an alternative fuel (e.g., deuterium only) by scaling the reaction rates for the two fuels.



A term sometimes used to indicate that component of a fusion power plant used to "breed", or produce via nuclear reactions, tritium from the energetic neutrons released, for use as fuel in the power plant. The most commonly used reaction is:-?


Bremsstrahlung radiation

Occurs in plasma when electrons interact (‘collide’) with the Coulomb fields of ions; the resulting deflection of the electrons causes them to radiate.



An ignited plasma is said to be "burning".



A transient enhancement of the solar radio emission, usually associated with an active region or flare.


Butterfly diagram

A plot of observed solar active region latitudes vs. time. This diagram, which resembles a butterfly, shows that the average latitude of active region formation drifts from high to low latitudes during a sunspot cycle.


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