Laser Heated Emissive Probes Design and Development under National Fusion Program and Potential Measurement

Emissive probes are the tools for the direct deter- mination of the plasma potential ~PL and they deliver a more reliable measure of φPL compared to the indi- rect measurements with cold Langmuir probes. The emissive probe works on the principle of compensating the well-known asymmetry of the I-V characteristic of a single cold Langmuir probe by an electron emission current from the probe into the plasma. In an ideal case, the saturated value of floating potential V（А,em） of a highly emissive probe should equal the plasma potential. A conventional emissive probe usu- ally consists of a loop of tungsten wire heated by an electric current passing through it. These conven- tional emissive probes containing an electric current- heated metal wire loop suffer a huge drawback when it comes to their lifetime. The metal wire used in these probes evaporates and subsequently breaks when heated with high current, leading to frequent replacements of these wires. When used in ultra high vacuum （UHV） plasma systems, frequent replacement of these wires requires frequent vacuum breaks in the plasma systems. In many plasma systems espe- cially in magnetized toroidal hot plasmas like toka- maks, where determination of the electric fields leads to a great deal of useful information, frequent breaking of the vacuum is impossible for changing the filament of the emissive probes. Hence, along with the other drawbacks of the conventional emissive probes such as limited emission current, bending in a magnetic field makes their use impractical in these plasma systems. The most suitable alternative is the emissive probes heated by a focused infra-red laser. Due to them having several advantages over the conventional emis- sive probes, laser heated emissive probes （LHEPs） are found to have more and more uses in plasma systems. The advantages of the LHEP are： longer lifetime （no filament breaking issues）, attainment of higher tem- perature without melting or evaporation and thus higher emissivity, no deformation of the pr     

Multipliers on Vector-valued L~1-spaces for Hypergroups

In this article, we extend the well known Wendel's theorem to the context of vector-valued L~1-spaces on hypergroups. In this regard, various cases have been studied.     

A graphical scheme for addressing determinants in large configuration interaction treatments

A graphical technique is proposed for generating and addressing all required α and β strings of spin-orbitals for configuration interaction treatments based on determinants. Compared with other treatments, this scheme, as well as reducing to a minimum the number of logical operations, avoids entirely the storage of the massive tables and vectors usually required for addressing the determinants. The generation is proposed of all required addresses to locate the determinants in the CI vectors, before and after application of the Hamiltonian, at run time using graphs and one intermediate table of acceptable dimensions. The scheme, which has been tested on a small personal computer, appears ideal when limited computational resources are available for the CI treatment. It is believed also to be useful for larger applications.     

Unpolarized coupled DGLAP evolution equation at small-x

In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small-x limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated t-evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-Q ² region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when Q ² increases for fixed values of x.