Plasmas, often called the fourth state of matter and the most common one in the universe, have parameters varying by many orders of magnitude, from temperature of a few hundred kelvin in the Earth's ionosphere to 1016 K in the magnetosphere of a pulsar. Ultracold plasmas, produced by photoionizing a sample of laser-cooled and trapped atoms near the ionization limit, have extended traditional neutral plasma parameters by many orders of magnitude, to electron temperatures below 1 K and ion temperatures in the tens of &mu K to a few Kelvin, and densities of 105 cm-3 to 1010 cm-3. These plasmas thus provide a testing ground to study basic plasma theory in a clean and simple system with or without a magnetic field. Previous studies of ultracold plasmas have primarily concentrated on temperature measurements, collective modes and expansion dynamics in the absence of magnetic fields.

This thesis presents the first study of ultracold plasma dynamics in a magnetic field. The presence of a magnetic field during the expansion can initiate various phenomena, such as plasma confinement and plasma instabilities. While the electron temperatures are very low in ultracold plasmas, we need only tens of Gauss of magnetic field to observe significant effects on the expansion dynamics. To probe the ultraocold plasma dynamics in a magnetic field, we developed a new diagnostic - projection imaging, which images the ion distribution by extracting the ions with a high voltage pulse onto a position-sensitive detector. Early in the lifetime of the plasma (< 20 &mu s), the size of the image is dominated by the time-of-flight Coulomb explosion of the dense ion cloud. For later times, we measure the 2-D Gaussian width of the ion image, obtaining the transverse expansion velocity as a function of magnetic field (up to 70 G),and observe that the transverse expansion velocity scales as B &minus1/2, explained by a nonlinear ambipolar diffusion model that involes anisotropic diffusion in two different directions.

We also present the first observation of a plasma instability in an expanding ultracold plasma. We observe periodic emission of electrons from an ultracold plasma in weak, crossed magnetic and electric fields, and a strong perturbed electron density distribution in electron time-of-flight projection images. We identify this instability as a high-frequency electron drift instability due to the coupling between the electron drift wave and electron cyclotron harmonic, which has large wavenumbers corresponding to wavelengths close to the electron gyroradius.