Motion in a Magnetic Field

Also in 1950 Sakliarov and Tamm proposed an idea for a controlled thermonuclear fusion reactor, the TOKAMAK (acronym for the Russian phrase for toroidal chamber with magnetic coiF ), which achieved the highest ratio of output power to input power of any fusion device of the twentieth centuiy. This reactor grew out of interest in a controlled nuclear fusion reaction, since 1950. Sakharov first considered electrostatic confinement, but soon came to the idea of magnetic confinement. Tamm joined the effort with his work on particle motion in a magnetic field, including cyclotron motion, drifts, and magnetic surfaces. Sakharov and Tamm realized that... 

Figure 5.5 The motion in a magnetic field B of the orbital angular momentum vector L.

Ion cyclotron resonance (ICR) is the excitation of the cyclotron frequency of ion motion in a magnetic field by an electric rf field at resonance. ICR spectrometry is based on the application of the resonance phenomenon to the detection of ions. 

Although it appears possible to measure the mass of a single kind of charged atom from its motion in a magnetic field, it is more practical to measure relative masses. An apparatus, Fig. 3.1, is set up so that H, Q, and o remain constant, making the mass of the ion proportional to the radius of its path ... 

The specularity of a 2DEG in a strong magnetic field is that the energy spectrum of the electrons is discrete due to orbital quantization of the cyclotron motion in a magnetic field. The energy spectrum can be written in the form [18] ... 

NMR depends on manipulating the collective motions of nuclear spins, held in a magnetic field. As with... 

Motion, and in particular diffiision, causes a further limit to resolution [14,15]. First, there is a physical limitation caused by spins diflfiising into adjacent voxels durmg the acquisition of a transient. For water containing samples at room temperature the optimal resolution on these grounds is about 5 pm. However, as will be seen in subsequent sections, difhision of nuclei in a magnetic field gradient causes an additional... 

Microwave discharges at pressures below 1 Pa witli low collision frequencies can be generated in tlie presence of a magnetic field B where tlie electrons rotate witli tlie electron cyclotron frequency. In a magnetic field of 875 G tlie rotational motion of tlie electrons is in resonance witli tlie microwaves of 2.45 GHz. In such low-pressure electron cyclotron resonance plasma sources collisions between tlie atoms, molecules and ions are reduced and the fonnation of unwanted particles in tlie plasma volume ( dusty plasma ) is largely avoided. 

The early development of electric motors and generators can be traced to the 1820 discovery by Hans Christian Oersted that electricity in motion generates a magnetic field. Oersted proved the long-suspected... 

Alternating-current motors are classified as induction motors or synchronous motors. Faraday found that a stationaiy wire in a magnetic field produced no current. However, when the wire continues to move across magnetic lines of force, it produces a continual current. When the motion stops, so does the current. Thus Faraday proved that electric current is only produced from relative motion between the wire and magnetic field. It is called an induced current—an electromagnetic induction effect. 

Fourier transform mass spectrometry is made possible by the measurement of an AC current produced from the movement of ions within a magnetic field under ultra-high vacuum, commonly referred to as ion cyclotron motion.21 Ion motion, or the frequency of each ion, is recorded to the precision of one thousandth of a Hertz and may last for several seconds, depending on the vacuum conditions. Waveform motion recorded by the mass analyzer is subjected to a Fourier transform to extract ion frequencies that yield the corresponding mass to charge ratios. To a first approximation, motion of a single ion in a magnetic field can be defined by the equation... 

Larmor precession The motion describing the rotation of the axis of the spin of a nucleus in a magnetic field. 

Image current detection is (currently) the only nondestructive detection method in MS. The two mass analyzers that employ image current detection are the FTICR and the orbi-trap. In the FTICR ions are trapped in a magnetic field and move in a circular motion with a frequency that depends on their m/z. Correspondingly, in the orbitrap ions move in harmonic oscillations in the z-direction with a frequency that is m/z dependent but independent of the energy and spatial spread of the ions. For detection ions are made... 

The equation of motion of a charged particle in a magnetic field of strength B is given by the following, where r is the radius of the circular track taken by the ion ... 

A nuclear spin has a magnetic moment y which, when placed in a magnetic field II, obeys the equation of motion,... 

Finally, let us consider the effect of applying an external magnetic field B (Kartsovnik, 2004). In a magnetic field, the motion of quasi-particles becomes partially quantized according to the expression ... 

Understanding flux motions and especially identifying the mechanism(s) for pinning at present remain a challenging opportunity. Measurements of a dissipation peak at near 45 K (well below Tc) in Bi-Sr-Ca-Cu-O samples oscillating in a magnetic field and interpreted... 

Electrons switch between levels characterized by Ms values. Let us examine now an ensemble of n molecules, each with an unpaired electron, in a magnetic field at a given temperature. The bulk system is at constant energy but at the molecular level electrons move, molecules rotate, there are concerted atomic motions (vibrations) within the molecules and, in solution, molecular collisions. Is it possible to have information on these dynamics on a system which is at equilibrium The answer is yes, through the correlation function. The correlation function is a product of the value of any time-dependent property at time zero with the value at time t, summed up to a large number n of particles. It is a function of time. In this case the property can be the Ms value of an unpaired electron and the particles are the molecules. The correlation function has its maximum value at t = 0 since each molecule has one unpaired electron, the product of the... 

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