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The upper critical field, $H_{c2}$, of Mg(B$_{1-x}$C$_x$)$_2$ has been measured in order to probe the maximum magnetic field range for superconductivity that can be attained by C doping. Carbon doped boron filaments are prepared by CVD techniques, and then these fibers are then exposed to Mg vapor to form the superconducting compound. The transition temperatures are depressed about $1 K/%$ C and $H_{c2}(T=0)$ rises at about $5 T/%$ C. This means that 3.5% C will depress $T_c$ from $39.2 K$ to $36.2 K$ and raise $H_{c2}(T=0)$ from $16.0 T$ to $32.5 T$. Higher fields are probably attainable in the region of 5% C to 7% C. These rises in $H_{c2}$ are accompanied by a rise in resistivity at $40 K$ from about $0.5 \mu \Omega cm$ to about $10 \mu \Omega cm$. Given that the samples are polycrystalline wire segments, the experimentally determined $H_{c2}(T)$ curves represent the upper $H_{c2}(T)$ manifold associated with $H\perp c$.

Superconducting magnesium diboride has been prepared with intra-granular TiB precipitates that have appropriate size and spacing for the pinning of superconducting vortices. The TiB particles have a size ranging from 1 nm to 20 nm and a spacing about 5 times as large. By co-depositing Ti and B on a commercial carbon coated silicon carbide substrate with chemical vapor deposition methods, it was possible to obtain a starting fiber with Ti well dispersed in the B. Reacting these fibers in a Mg vapor then transformed the fiber into a superconductor capable of carrying 10,000 A/cm^2 at 25K and 1 T. The Ti-B bonds are strong enough that there is relatively little migration of the Ti as the MgB2 grains form around the TiB precipitates. TiB2 precipitates, if they are present, can not be seen in the selected area diffraction pictures that show the TiB precipitates., 6 pages, 4 figures. Applied Physics Letters (ssubmitted)

Vortex fluctuations in the $La_{2-x}Sr_{x}CuO_{4+\delta}$ system have been studied as a function of magnetic field, temperature and carrier concentration in order to determine the dimensionality of the fluctuations. For a $x=0.10$ sample, there is a unique crossing-temperature on the magnetization vs. temperature plots for all magnetic fields up to 7 T, and the data scale very well with 2D fluctuation theory. At lower x-values where $H_{c2}$ is much smaller, there are two well defined crossing points, one at low fields (typically less than 1 T) and another at high fields (typically 3-7 T). A fit of the data to fluctuation theory shows that the low field crossing data scale as 2D fluctuations and the high field crossing data scale as 3D fluctuations. It would appear that as the magnetic field approaches $H_{c2}$, there is a 2D to 3D cross-over where the low field 2D pancake vortex structure transforms into a 3D vortex structure.

Transport and thermodynamic properties of a sintered pellet of the newly discovered $MgB_2$ superconductor have been measured to determine the characteristic critical magnetic fields and critical current densities. Both resistive transition and magnetization data give similar values of the upper critical field, $H_{c2}$, with magnetization data giving $dH_{c2}/dT=0.44~T/K$ at the transition temperature of $T_c=40.2 K$. Close to the transition temperature, magnetization curves are thermodynamically reversible, but at low temperatures the trapped flux can be on the order of one Tesla. The value of $dH_c/dT$ at $T_c$ is estimated to be about $12~mT/K$, a value similar to classical superconductors like Sn. Hence, the Ginsburg-Landau parameter $\kappa \sim 26$. Estimates of the critical supercurrent density, $J_c$, using hysteresis loops and the Bean model give critical current densities on the order of $10^5~A/cm^2$. Hence the supercurrent coupling through the grain boundaries is comparable to intermetallics like $Nb_3Sn$.

We present a detailed magneto-optical investigation of the magnetic flux penetration in polycrystalline MgB2 slabs made by direct reaction of B and Mg. Our results unambiguously indicate a uniform, Bean critical state magnetization behavior with almost no electromagnetic granularity. From the measured magnetic flux profiles we were able to extract the temperature dependence of the critical current density Jc(T). The Jc(T) value reaches 1.8x10^5 A/cm2 at 10K and 0.12T, in good agreement with global magnetization measurements.