Dictionary of Material Science and High Energy Physics Part 7 pot

With the use of the ion acoustic speed, the dispersion relation of the ion acoustic wave with frequency ω and wave number k is given by ω = kc s.. As the wave propagates into a decreasin

where A is the amplitude, α, β are constants,

t is the time, and x is the position Hence,

as the amplitude increases the speed increases,

while the width shrinks Solitons are related to

shock waves through a quasi-potential called the

Sagdeev potential

ion acoustic wave The only normal mode

of ions allowed in nonmagnetized plasmas, ion

acoustic waves are essentially driven by

ther-mal motions of both electrons and ions In fact,

their phase and group velocities are given by

the ion acoustic or sound speed cs = {(KT e+

3KT i )/m i}1/2 , where K is the Boltzman

con-stant, T e , and T i are the electron and ion

tem-peratures, and m i is the ion mass With the use

of the ion acoustic speed, the dispersion relation

of the ion acoustic wave with frequency ω and

wave number k is given by ω = kc s There

are two damping mechanisms for ion acoustic

waves; one is Landau damping and the other is

the non-linear Landau damping that occurs

af-ter trapping of particles inside the electrostatic

wave potential of relatively large ion acoustic

waves Ion acoustic waves are heavily damped

if Te < Ti, so that such waves usually propagate

only in plasmas with Ti  T e Various

non-linear states of ion acoustic waves have been the

subjects of intensive research in plasma physics

for many years As they are amplified, these

waves may form solitons, double layers, and

shock waves See also ion wave

ion beam instabilities There are several

in-stabilities driven by an ion beam, which, in a

magnetized plasma, usually propagates along an

external magnetic field Electrostatic

instabili-ties are the ion acoustic instability driven by the

relative drift between the electrons and the beam

ions and the ion–ion drift instability The

for-mer generates principally field-aligned waves,

and the latter generates either field-aligned or

oblique waves Among electromagnetic

insta-bilities are the ion–ion resonant and nonresonant

instabilities; the former excite right-hand

circu-larly polarized waves, and the latter excite

left-hand circularly polarized (Alfvén) waves at

rela-tively low drift speeds, i.e., the fire-hose

instabil-ity and right-hand circularly polarized waves at

higher speeds Whistler waves can also be

gen-erated Production of these right-hand circularly

polarized waves can be enhanced by increaseddrift speed as well as increased perpendiculartemperature of the beam

ion cyclotron resonance See cyclotron

res-onance

ion cyclotron resonance heating (ICRH)

Has been utilized to heat plasmas by netic waves For this scheme, an electromag-netic ion cyclotron wave is launched from anexternal source into a plasma with a frequency

electromag-ω, which is lower than the local ion cyclotron frequency  i of the target plasma As the wave

propagates into a decreasing magnetic field, itwill eventually heat the target plasma efficientlythrough cyclotron acceleration when the local

resonance condition ω =  i is satisfied This

heating scheme is frequently used in several sion devices such as tokamaks

fu-ion cyclotron wave When magnetized,

plas-mas can support electrostatic ion cyclotron

waves that propagate nearly perpendicular to

the external magnetic field The dispersion

re-lation is given by ω2 = 2

i + k2c s , where ω2

is the frequency, k is the wave number of the wave,  i is the ion cyclotron frequency, and c2s

is the ion acoustic speed Experimentally, ion

cyclotron waves were first observed by Motley

and D’Angelo in a device called a Q-machine

On the other hand, electromagnetic ion

cy-clotron waves propagate predominantly along

the magnetic field, and are left-hand polarized.These waves are frequently used to heat ions inplasma confinement devices, i.e., ion cyclotronresonance heating (ICRH) See also ion wave

ionic bonding The bonding in structures thatresults from the net attraction between oppo-sitely charged species For example, in com-pounds of the alkalis and a halogen atom (e.g.,sodium chloride, NaCl), the chlorine atom de-taches an electron from the sodium atom, form-ing Na+and Cl−ions which together can form

a stable configuration or crystal structure Thevariation of the energy of the (Na++ Cl−) sys-

tem, E s (R), relative to the sum of the energies

of the isolated neutral atoms is given as

E s (R) = E s ( ∞) − 1

R + Ae −hR

flected light by 90◦with respect to the incident

light, and therefore the reflected light is blocked

by the polarizer Rotation of the polarization is

generally achieved by using Faraday rotation in

magneto-optical material Optical isolators are

very common in optical communications

sys-tems

isomer (1) One of two or more nuclides that

have the same atomic and mass numbers but

dif-fer in other properties

(2) A nucleus which has the same proton and

neutron number as in other nucleus, but which

has a different state of excitation

isomer (nuclear) An excited state of a

nu-cleus which has a measurable mean life The

radioactive decay of such a state is said to occur

in an isomeric transition and the phenomenon is

known as nuclear isomerism

isoscalar particle A particle with isospin

equal to zero

isospin A property (or quantum number)

which distinguishes a proton from a neutron

With respect to the nuclear force, a proton and

a neutron behave in essentially the same way

In contrast protons and neutrons interact

differ-ently with a Coulomb field With an isospin of

1

2 assigned to the nucleon, the two nucleons are

then distinguishable through the third

compo-nent of the isospin being+1

2for the proton and

−1

2for the neutron

isothermal bulk modulus (β T) A measure of

the resistance to volume change without

defor-mation or change in shape in a thermodynamic

system in a process at constant temperature It

is the inverse of the isothermal compressibility

isothermal compressibility (κ T) The

frac-tional decrease in volume with increase in

pres-sure while the temperature remains constant

dur-ing the compression

isothermal process A process at constanttemperature

isotone One of two or more nuclides that havethe same number of neutrons in their nuclei butdiffer in the number of protons

isotope One of two or more nuclides that havethe same atomic number but different numbers

of neutrons so that they have different masses.The mass is indicated by a left exponent on thesymbol of the element (i.e.,14C)

isotope effect The correction to the energylevels of a bound-state system due to the finitemass of the nucleus

isotope effect (superconductivity) Early inthe development of the theory of superconduc-tivity, it was found that different isotopes of thesame superconducting metal have different crit-

ical temperatures, T c, such that

TcM a= constant

where M is the mass of the isotope and a ≈ 0.5

for most metals This effect made it clear that thelattice of ions in a metal is an active participant

in creating the superconducting state

isotropic Independent of direction, or ically symmetric

spher-isotropic turbulence Implies that there is nomean shear and that all mean values of quanti-ties such as turbulence intensity, auto- and cross-correlations, spectra, and higher order correla-tion functions of the flow variables are indepen-dent of the translation or rotation of the axes ofreference These conditions are not typical inreal flows On the other hand, assumptions of

isotropic and homogeneous turbulence have led

to understanding of many aspects of turbulentflows

isotropy Having identical properties in alldirections

isovector particle A particle with isospinequal to one and, thus, three possible chargestates corresponding to the three possible val-

ues (0,±1) of the third component of the isospin

vector

ITER Originally proposed at a summit

meet-ing between the USA and the USSR in 1985, the

purpose of the international thermonuclear

ex-perimental reactor [ITER] project is to build a

toroidal device called a tokamak for magnetic

confinement fusion to specifically demonstrate

thermonuclear ignition and study the physics of

burning plasma The initial phase of this project

was jointly funded by four parties: Japan, the

European community, the Russian Federation

and the United States In July of 1992, ITER

engineering design activities [ITER EDA] wereestablished to provide a fully integrated engi-neering design as well as technical data for fu-ture decisions on the construction of the ITER

To meet the objectives, the linear dimensions ofITER will be 2–3 times bigger than the largestexisting tokamaks According to the 1998 de-sign, the major parameters of the ITER are asfollows: total fusion power of 1.5G W, a plasmainductive burn time of 1000 s, a plasma majorradius of 8.1 m, a plasma minor radius of 2.8 m,

a toroidal magnetic field at the plasma center of5.7 T, and an auxiliary heating power by neutralbeam injection of 100 MW

Jacobi coordinates In describing the

dynam-ics of many-particle systems, we are often faced

with the task of choosing an appropriate set of

coordinates For example, in the two-body

prob-lem, the motion relative to the center of mass is

described by the one-body Schrödinger

m1+m2 is the reduced mass for particles

of mass m1 and m2, and r = r1− r2 are the

relative position vectors of particles 1 and 2

Suitable sets of center-of-mass coordinates can

be similarly constructed for systems containing

any number of particles For example, consider

the three-body problem

A set of Jacobi coordinates for a three-body system.

We first consider particles 1 and 2 as a

sub-system with relative coordinate r and center of

mass µ The motion of the center-of-mass of

this sub-system relative to the third particle is

described through the second position vector ρ.

The Schrödinger equation for this system then

are called Jacobi coordinates.

Jahn Teller effect (rule) A non-linear ecule in a symmetric configuration with an or-bitally degenerate ground state is unstable Themolecule will seek a less symmetric configu-ration with an orbitally nondegenerate groundstate Although this rule was introduced to de-scribe molecules, it has applications to impuri-ties and defects in solids An impurity ion canmove from a symmetric position in a crystal to aposition of lower symmetry to lower its energy

mol-A free hole in an alkali halide crystal (such asKCI) can be trapped by a halogen ion and be-comes immobile; it moves only by hopping toanother site if thermally activated

Jansky, K. Astronomers have alwayssearched for ways of studying celestial objectslike comets, stars, and galaxies One of themost widely used methods of studying objects

in the sky is through the electromagnetic ation reaching us from these objects Because

radi-of the absorption radi-of electromagnetic radiationpropagating from outer space to us, we can onlyuse limited bands (ranges of frequencies) One

band was discovered in 1931 by K Jansky He

discovered radio waves coming from the MilkyWay This discovery was very ground-breaking

as it opened up a new field called omy, through which new discoveries about theuniverse such as pulsars, quasars and the univer-sal radiation at 3 K have been made

radioastron-Jaynes–Cummings model (1) Describes

dy-namics of a two-level atom interacting with asingle mode of radiation field in a lossless cav-ity This model is perhaps the simplest solvablemodel that describes the fundamental physics

of radiation–matter interaction This somewhatidealized model has been realized in the labo-ratory by using Rydberg atoms interacting withthe radiation field in a high-Q microwave cav-

ity The Hamiltonian for the Jaynes–Cummings

model in the rotating-wave approximation is

given by

ˆ

H = 1

2¯hω0ˆσ3+ ¯hω ˆa†ˆa + 1/2+ ¯hλˆσ+ˆa + ˆa†ˆσ− .

Here, the Pauli matrices ˆσ+, ˆσ−, and ˆσ3

repre-sent the raising, lowering, and inversion

opera-tors for the atom, ω0is the transition frequency

for the atom, and ω is the field frequency

Oper-atorsˆa†andˆa are the creation and annihilation

operators of the field-satisfying boson

commu-tation relations

(2) The simplest model in cavity quantum

electrodynamics In the Jaynes-Cummings

mod-el, one assumes that a two-level atom with upper

level|a and lower level |b interacts with only

one mode of the quantized electromagnetic field

Furthermore, this mode is assumed to be

reso-nant with the atomic transition frequency The

Hamilton operator in the rotating wave

approx-imation for this problem is given by

H =ω0b†b+1

2¯hω0σz + ¯hgbσ++ b†σ−

Here g is the coupling constant, ω0is the reso-

nant transition frequency of the atoms, and σ+,

σ−, and σzare the well-known Pauli spin

matri-ces This reflects the possibility of interpreting a

two-level system as a spin 1/2 system with spin

up when the population is in the upper state and

spin down for a population of the lower state

The first two terms of the Hamiltonian

de-scribing the energy eigenstates of the photons

and the two-level atom commute with the

sec-ond part describing the interaction of the

sys-tem This results in the possibility of writing

the eigenstates for the Hamiltonian as a

combi-nation of the eigenstates of the atom and field

The eigenstates and eigenvalues for such a

system are given by

where n is the number of photons in the field.

The eigenvalues for these states are±¯h, where

2=2+ 4g2(n + 1)

is called the Rabi frequency A possible ing of the quantized cavity field with the atomic

detun-resonance  is also taken into account here

As-suming that the atom is initially in the excited

state and the field has n photons, one can

cal-culate the probability of finding the atom in the

excited state and the atom in a state with n tons at time t to

super-Of greatest interest is the strong coupling

limit where the coupling g is stronger than the

dissipation processes of the cavity and the taneous decays of the atomic levels

spon-The Jaynes-Cummings model is the basis for

the micromaser experiments, where a single

at-om interacts with a high-Q cavity The two-levelcharacteristics of the atom are approximated byexciting the atom into a Rydberg state before en-tering the cavity The interaction time can be de-termined by using velocity selective excitationinto the Rydberg states Pure quantum phenom-ena such as quantum collapse and revival can beobserved

Jeans instability A plasma under the ence of a gravitational force is unstable due to

influ-the Jeans instability, for which waves longer

than the Jeans length grow exponentially Thisphenomenon is analogous to ordinary plas-

ma waves propagating without being damped, provided that their wavelengths are suf-ficiently long

Landau-Jeans, Sir J. Sir J Jeans, together with Lord

Rayleigh, derived a spectral distribution tion to describe black-body radiation Their the-ory was called the Rayleigh–Jeans theory andcould only explain the long-wavelength behav-ior of the spectrum They derived a spectral

func-function ρ (λ, T ), where λ is wavelength and

T is temperature, for the radiation emitted from

an enclosed cavity (black-body) using the laws

of classical physics They modeled the thermalwaves in the cavity as standing waves (modes)

of wavelength λ They calculated the number

of modes per unit of volume in the wavelength

Rayleigh and Jeans surmised that the

stand-ing waves are caused by constant absorption and

emission of radiation of frequency ν by

classi-cal linear harmonic oscillators in the walls of

the cavity They assumed that the energy of

each oscillator can take any value from 0 to∞,

which turned out to be an erroneous

assump-tion The average energy of a collection of such

oscillators was calculated, using classical

sta-tistical mechanics, to be k B T , where k B is the

Boltzmann constant Thus, they predicted the

black-body distribution to be

ρ (λ, T )=8π

λ4k B T

This is the Rayleigh–Jeans law It agrees only

in the long-wavelength limit and diverges for

λ→ 0

jellium A model in which the positive

charges of the ions in a metal are uniformly

spread (like jelly) in the volume occupied by the

ions It is the closest realization of the Thomson

atom

jellium model Used in the study of the

cor-relation effects in an electron gas The basic

premise is that the atoms in the lattice are

re-placed with a uniform background of positive

charge

jet Efflux of fluid from an orifice, either

two-or three-dimensional In the ftwo-ormer case, the

jet is emitted from a slit in a wall In the latter

case, the jet exits through a hole of finite size.

Jets expand by spreading and combining with

surrounding fluid through entrainment A jet

may either be laminar or turbulent

JET The Joint European Torus (JET)

lo-cated at Abingdon in Oxfordshire, England is a

toroidal tokamak-type device for magnetic

con-finement fusion jointly operated by 15 European

nations The JET project was set up in 1978,

and there are approximately 350 scientists, neers, and administrators supported by a similarnumber of contractors Even though the project

engi-was officially terminated in 1999, the JET

fa-cilities have still been in operation since then.This device, being the largest of its kind in theworld as well as the first to achieve the breakeven condition (input power = output power), is

of approximately 15 meters in diameter and 12meters high The central portion of the device

is a toroidal vacuum vessel of major radius 2.96meters with a D-shaped cross-section of 2.5 me-ters by 4.2 meters; the toroidal magnetic field atthe plasma center is 3.45T, and the plasma cur-rents are 3.2–4.8 MA It also has an additionalheating power of over 25MW It is presently theonly device in the world which is capable ofhandling as its fuel the deuterium–tritium [DT]mixtures used in a future fusion power station

jet instability From linear stability theory,jets are unstable above a Reynolds number offour, similar to Kelvin–Helmholtz instability.The resulting jet motion consists of vorticalstructures which roll up with surrounding fluidand dissipate downstream

jet pump Similar in design to an aspirator,except both working fluids are usually of thesame phase

jets in nuclear reactions Back-to-backstreams of hadrons produced in nuclear reac-tions Jets are usually observed when quarksand antiquarks (free for just a very short time)fly apart This can be observed, for example,

through the reaction e++e−→ γ → q + ¯q →

hadrons When the quarks reach a separation

of about 10−15 m, their mutual strong action is so intense that new quark-antiquarkpairs are produced and combine into mesons andbaryons, which emerge in two (and sometimesthree) back-to-back jets

inter-j–j coupling A possible coupling scheme forspins and angular momenta of the individual nu-

cleons in a nucleus In the j − −j scheme, (as

opposed to the LS scheme), first the intrinsic

spin and orbital angular momentum of each cleon are added together to yield the total an-gular momentum of a single nucleon Then the

nu-angular momenta of the individual nucleons are

summed up to give the total angular momentum

of the nucleus

j-meson/resonance Also known as the 

meson Particle discovered in 1974, which

con-firmed the existence of the fourth quark (the

charm quark)

Johnson noise Noise in an electric circuit

arising due to thermal energy of the charge

car-rier Noise power P generated in the circuit due

to the Johnson noise depends on the

tempera-ture T and frequency band ν considered, but

is independent of the circuit elements

exp[−hν/kT ] − 1 ,

where k is the Boltzmann constant For kT >>

hν, the noise power can be approximated to be

kT ν This noise can be reduced by cooling

the components generating the noise It is also

called Nyquist noise

Jones calculus Introduced by R Clark Jones

to describe the evolution of a polarization state

when it passes through various optical elements

In the Jones matrix formulation, the polarization

of a plane wave is represented by a pair of

com-plex electric field components E1and E2, along

two mutually orthogonal directions transverse to

the direction of propagation, written as a column

The action of various polarizing elements is then

described by complex 2× 2 matrices which act

on the column matrix representing the

polariza-tion state For example, the Jones matrix for a

quarter wave plate whose fast axis is horizontal

Jones matrix 2×2 matrix which describes

the effect of an optical element on the tion of light The polarization of the light can

polariza-be descripolariza-bed with a two-dimensional Jones tor Horizontal and vertical polarization can bedescribed as two vectors

vec-10

For a linear retarder, which introduces a

phase-shift of δ to one polarization direction and is aligned so that the optic axis makes an angle θ with respect to the horizontal, we find a Jones

polariza-al space These vectors can be expressed as asuperposition of two basis vectors The coeffi-cients for the two vectors can be written as thecomponents of a two-dimensional vector, which

is called a Jones vector Vertical and horizontal

polarization can then be represented as1

matrix

An alternative basis for describing the ization properties is via left and right circularpolarized light These can be written as1

Jones zones Volumes in k space (reciprocal

lattice) bounded by planes which are

perpendic-ular bisectors of reciprocal lattice vectors (as in

the case of the Brillouin zones) These planes

correspond to strong Bragg reflection for x-rays

Strong x-ray scattering suggests strong Bragg

reflection for electron waves and the presence of

large Fourier coefficients V (G) for the potential

which the electron sees, where G is the

recipro-cal lattice vector involved This means that if the

Jones zone is nearly filled with electrons, those

electrons near the zone boundary within an

en-ergy interval of approximately 1/2 |V (G)| will

lower their energy by approximately |V (G)|,

or |V | for short, each below the free

elec-tron energy The net energy reduction for the

electron gas is approximately 1/2N (E f ) |V |2,

where N (E f ) is the electron density of states at

the Fermi energy E f which gives a binding

en-ergy of 3/4 |V |2/E f per electron This method

can be applied even to a covalent crystal such

as diamond, silicon, or germanium Direct

lat-tice is a face-centered cubic with cube side a,

and has two atoms per unit cell separated by

the vector τ = (1, 1, 1)a/4 The Fourier

coeffi-cient V (G) of the crystal is that of a monoatomic

crystal V0(G) multiplied by the structure factor

(1 + exp(−iG • τ), which we call S(G) Since

reciprocal space is a body-centered cubic lattice

with side (2/a)2π , we see that the eight

recip-rocal lattice vectors (2π/a)( ±1, ±1, ±1) give

|S|2 = 2 and will define a Jones zone which can

accommodate (9/8)N states for each spin

direc-tion (and not N as we always have for Brillouin

zones) Here, N is the number of unit cells

(Bra-vais) of direct lattice A larger Jones zone can

be constructed from the twelve reciprocal lattice

vectors of the type 4π/a( ±1, ±1, 0), which can

accommodate all the valence electrons of the

crystal (8N ) Such ideas might explain the

sta-bility of certain metals and alloys See nearly

free electrons

Jönsson, C. The wave behavior of electrons

was demonstrated in 1961 by C Jönsson in an

electron diffraction experiment

Jordan, P. Two equivalent formulations of

quantum mechanics were put forward at about

the same time between 1924–1926 The first

formulation, called wave mechanics, was

devel-Jönsson used 40 keV electrons The slits were made

in a copper foil and were very small∼0.5 microns wide and the slit separation∼2 microns Interference fringes were observed on a screen at a distance of 0.4

m from the slits Since the fringe separation was very small, an electrostatic lens was used to magnify the fringes.

oped by E Schrödinger The other is matrixmechanics, which was developed by W Heisen-berg, M Born, and P Jordan

Josephson, B.D. In 1962, B.D Josephson

published a paper predicting two fascinating fects of superconducting tunnel junctions Thefirst effect was that a tunnel junction should beable to sustain a zero-voltage superconducting

ef-dc current The second effect was that if thecurrent exceeds its critical value, the junctionbegins to generate high-frequency electromag-netic waves

Josephson effect (1) (i) DC effect: In a

Josephson junction, an insulating oxide layer issandwiched between two superconductors

In each superconductor, electrons condenseinto Cooper pairs, which tunnel through the in-sulating layer We define a wave function, alsocalled an order parameter, for each superconduc-tor In superconductor 1, the order parameter iswritten as

1(x, t ) = n s1e −iφ1

φ1= φ s1 + ωt

where φ s1is the phase of the time-independentpart of the order parameter Similarly, for su-

Josephson junction made from two superconductors

separated by a thin oxide layer.

perconductor 2,

2(x, t ) = n s1e −iφ2

φ2 = φ s2 + ωt

n s is the number density of Cooper pairs in the

left and right superconductors, which is assumed

to be the same Using the familiar expressions

for current in terms of the wave functions  1,2

that are used in studying tunnelling in potential

barriers, we obtain the current J as

J = J0sin θ where θ = φ1− φ2 Thus a DC current flows

across the barrier if there is a phase gradient

(ii) AC effect: If a voltage V is applied across

the junction, there is a change in the energy of

the Cooper pairs, resulting in a change in the

phase of the time-dependent part of the order

(2) A Josephson junction can be made of two

good superconductors separated by a thin layer

of 10 Å of an insulator, and a normal conducting metal) or weaker superconductor Acurrent of Cooper pairs (bound electron pairs)would flow across the junction even if there is nopotential difference (voltage) between the two

(nonsuper-good superconductors If a DC voltage V0 isapplied, an oscillating pair current of angularfrequency|qV0/ h| results where q is the charge

on the Cooper pair (twice e, the electron charge) and h is Planck’s constant divided by 2π If, in addition to V0, we add an oscillatory voltage

v sin ωt, we find that the pair current J is given

by

J ≈ sin [δ0+ (qV0t / h) + (qv/hω) sin ωt] ,

where δ0 is a constant This formula predicts

that when ω = (qV0/ hn), where n is an integer,

there will be a DC current component present.Two or more Josephson junctions can be con-nected in parallel in a magnetic field, and theircurrent displays interference effects similar tothose of diffraction slits in optics

Josephson radiation If a DC current greaterthan the critical current flows through a Joseph-son junction, it causes a voltage V(t) to appear

Variation of the voltage V(t) across a Josephson tion versus ωt.

junc-across the junction which oscillates with time.This causes the emission of electromagnetic ra-

diation of frequency ω, such that the average

voltage across the junction, V, is given as

2eV = ¯hω

The first experimental observation of

Joseph-son radiation was reported in 1964 by I.K

Yan-son, V.M Svistunov, and I.M Dmitrenko The

English translation of this paper appears in Sov.

Phys JETP, 21, 650, 1965.

Josephson vortices Consider the following

Josephson junction in a magnetic field H0:

Josephson junction in a magnetic field H0.

If the junction is placed in a magnetic field

H0 directed along the z-axis, a screening

super-current is generated at the outer surfaces of each

slab Such current is constrained to flow within a

thin layer The magnetic field at x can be shown

to be proportional to dφ dx , where φ is the phase

difference between the superconductors The

differential equation which describes φ (Ferrell–

Prange equation) is

d2φ

dx2 = 1

λ2J sin φ where λJ is the Josephson penetration depth and

gives a measure of penetration of the magnetic

field into the junction In a weak magnetic field,

the above equations give solutions for the phase

difference φ and magnetic field H as

φ (x) = φ(0) exp (−x/λ J ) H(x)= H0 exp ( −x/λ J )

If the external field increases beyond a

cer-tain critical value which is characteristic of the

junction, the magnetic field penetrates into the

junction in the form of a soliton or vortex This

is called a Josephson vortex.

Joukowski airfoil See Zhukhovski airfoil

joule Unit of energy in the standard

interna-tional system of units

Joule effect (Joule magnetostriction) Change

in the length of a ferromagnetic rod in the rection of the magnetic field when magnetized

am-Joule–Thompson effect A process in which

a gas at high pressure moves through a porousplug into a region of lower pressure in a ther-mally insulated container The process con-serves enthalpy and leads to a change in tem-perature

j-symbols Symbols used in the context of

an-gular momentum algebra in quantum

mechan-ics For example, the symbol < j1j2m1m2|J M

>indicates the coupling of the two angular

mo-menta j1 and j2to a total angular momentum

J In this framework, m1, m2, and M are the

magnetic quantum numbers associated with thecomponent of their respective angular momentaalong a pre-chosen direction

JT-60 In September 1996, the breakeven

plas-ma condition (input power= output power) was

first achieved by JT-60, which proved the

fea-sibility of a fusion reactor based on the mak scheme Located in Naka, Japan, and op-erated by Japan Atomic Energy Research Insti-

toka-tute[JAERI], JT-60, a toroidal device for

mag-netic confinement fusion, is one of the largesttokamak machines in the world JT-60U, the

upgraded version of JT-60 had a negative-ion

based neutral beam injector installed in 1996,and the divertor transformed from open into W-shaped semi-closed in 1997 The major param-

eters of JT-60 are as follows: a plasma major

radius of 3.3 m, a plasma minor of radius 0.8 m,

a plasma current of 4.5M A, a toroidal magnetic

field at the plasma center of 4.4 T, and an

auxil-iary heating power by neutral beam injection of

30 MW

JT-60U at JAERI.

jump conditions Variation in Mach number

and other flow variables across a shock wave

For a normal shock wave, a variation in Mach

number across a shock is only a function of the

upstream Mach number as

M22= (γ − 1)M

2

1+ 2

2γ M12− (γ − 1) where γ is the ratio of specific heats For M1=

1, M2 = 2; this is the weak wave limit where

the wave is a sound wave For M1∞, M2 =

√

(γ − 1)/2γ ; this is the infinite limit which

shows that there is a lower limit which the

sub-sonic flow can attain For air, γ = 1.4; this

becomes M2 = 0.378 Thus, the Mach

num-ber (but not the velocity) can go no lower than

this limit The jump in density and velocity is

related by the continuity equation

to-T02

T01 = 1

The above relations show that pressure, sity, and temperature (hence, speed of sound)all increase across a shock wave, while the Machnumber and total pressure decrease across ashock

den-junction (i) p–n: Formed when a ductor doped with impurities (acceptors) is de-posited on another semiconductor doped withimpurities (donors) It should be noted that asemiconductor doped with donors is called ann-type semiconductor, and those doped with ac-ceptors are called p-type semiconductors Asemiconductor doped with acceptors possessesholes in its valence band For example, sup-pose a small percentage of atoms in pure sil-icon are replaced by acceptors like gallium oraluminium Gallium and aluminium each havethree valence electrons occupying energy levelsjust above the valence band of pure silicon (∼0.06 eV) It is energetically favorable for an elec-tron from a neighboring silicon atom to becometrapped at the acceptor atom, forming an Al−or

semicon-Ga−ion This electron originates from the

va-lence band and leaves a vacancy or hole in thisband Such holes can carry a current which dom-inates the intrinsic current of the host Donorimpurities in silicon have five valence electrons.Each of the electrons can form a covalent bondwith one of the four valence electrons in a siliconatom This leaves an extra unpaired electron that

is loosely bound to the donor atom The energylevels of this extra electron lie close to the con-duction band of silicon (∼ 0.05 eV below) andcan thus be excited to the conduction band andadded to the number of charge carriers Some

uses of the p–n junction are in making solar cells,

rectifiers, and light-emitting diodes

(ii) p–n–p: Type of junction is often used

as an amplifier in transistors It consists of ann-type semiconductor sandwiched between twop-type semiconductors Small changes in theapplied voltage cause changes in the emitter cur-rent For Vin VE, the change in the collector

current is given by

IC= ηIE

where η is a measure of the fraction of the emitter

current reaching the collector, and IE is the

change in the emitter current due to a change in

Vin(Vin) The resulting amplification is then

given byVout

Vin and can be in excess of 100 p-n-p junction as an amplifier.