ECR heating on the WEGA stellarator

The plasma in the WEGA stellarator is generated and heated by Electron Cyclotron Resonance Heating (ECRH). The microwave is emitted from the low field side mid-plane with power of up to 6+20 kW and with a frequency of 2.45GHz (λ=12.45 cm). The low cut-off density of ncutoff=7.5×10¹⁶m⁻³ makes ECRH on the WEGA stellarator inefficient in both O-mode and X-mode regime. This was confirmed in the first experimental campaign by perpendicular launch of the microwave with a TE11 antenna. In these experiments only edge heating was observed. Density and temperature profiles were hollow [1]. For the over dense plasma heating, mode conversion into the electrostatic electron Bernstein waves (EBW) is required. Two schemes have been tested: the direct X-B (X-mode to Bernstein mode) conversion, where an X-wave must be launched perpendicular to the magnetic field into an over dense plasma with a steep density gradient. In these experiments the strong reflection of the microwave power at the cut-off layer prohibited efficient plasma heating. Another possibility is the O-X-B conversion scheme [2]. The methods of its achievement with different antennas are the subject of this paper.Плазма у стеллараторі WEGA утворюється та нагрівається за допомогою НВЧ-нагріву на електронно- циклотронній частоті (ЕЦР). Ввід НВЧ-енергії здійснюється із зовнішнього боку тору у його екваторіальній площині, на частоті 2.45 ГГц (λ=12.45 см) та з максимальною потужністю до 26 кВт. Низька критична щільність плазми для цієї частоти (ncutoff=7.5×10¹⁶м⁻³ ) робить традиційний ЕЦР-нагрів неефективним, як у режимі «Звичайної» (З-хвиля), так і у режимі «Незвичайної» хвилі (Н-хвиля), що було підтверджено у ході першої експериментальної кампанії, коли НІЧ-енергія вводилась перпендикулярно силовим лініям магнітного поля за допомогою циліндричного ТЕ11 хвилеводу. У цих експериментах спостерігався нагрів периферичної плазми, профілі щільності та температури мали порожній характер [1]. Для нагріву плазми з щільністю вище щільності відсічки необхідна трансформація в електростатичну Бернштейн хвилю (ЕБХ). Два сценарії нагріву було випробувано на установці: перший з трансформацією Н-хвилі у ЕБХ, в цьому випадку Н-хвиля повинна бути введена перпендикулярно магнітному полю в плазму з щільністю, яка перевищує критичну. У цих експериментах сильне відбиття НВЧ-енергії у шарі відсічки перешкоджало ефективному нагріву плазми. У другому випадку використовується сценарій з подвійною конверсією спочатку З-хвилі у Н-хвилю з наступною трансформацією Н-хвилі в ЕБХ [2]. Методи реалізації такого сценарію і є темою цієї роботи.Плазма в стеллараторе WEGA создается и нагревается при помощи СВЧ-нагрева на электронно- циклотронной частоте (ЭЦР). Ввод СВЧ-энергии производится с внешней стороны тора в его экваториальной плоскости на частоте 2.45 ГГц (λ=12.45 см) и с максимальной мощностью до 26 кВт. Низкая критическая плотность плазмы для данной частоты (ncutoff=7.5×10¹⁶м⁻³ ) делает традиционный ЭЦР-нагрев неэффективным, как в режиме «обыкновенной» (О-волна), так и в режиме «необыкновенной» волны (Н-волна), что было подтверждено в ходе первой экспериментальной кампании, когда СВЧ-энергия вводилась перпендикулярно силовым линиям магнитного поля при помощи цилиндрического ТЕ11 волновода. В этих экспериментах наблюдался нагрев периферийной плазмы, профили плотности и температуры имели полый характер [1]. Для нагрева плазмы с плотностью, выше плотности отсечки, необходима трансформация в электростатическую Бернштейн волну (ЭБВ). Два сценария нагрева были протестированы на установке: первый с непосредственной трансформацией Н-волны в ЭБВ, в этом случае Н-волна должна быть запущена перпендикулярно магнитному полю в плазму с плотностью, превышающей критическую. В этих экспериментах сильное отражение СВЧ- энергии в слое отсечки препятствовало эффективному нагреву плазмы. Во втором случае используется сценарий с двойной конверсией сначала О-волны в Н-волну с последующим превращением Н-волны в ЭБВ[2]. Методы реализации такого сценария и есть тема настоящей работы

A consistent analysis of (e,e'p) and (d,3He) experiments

The apparent discrepancy between spectroscopic factors obtained in (e,e'p) and (d,3He) experiments is investigated. This is performed first for 48Ca(e,e'p) and 48Ca(d,3He) experiments and then for other nuclei. It is shown that the discrepancy disappears if the (d,3He) experiments are re-analyzed with a non-local finite range DWBA analysis with a bound-state wave function that is obtained from (e,e'p) experiments.Comment: 23 pages, 7 figure

Semigroup Closures of Finite Rank Symmetric Inverse Semigroups

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations $\mathscr{I}_\lambda^n$ of the rank $\leqslant n$ is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related results about the nonexistence of (partial) compactifications of classes of semigroups that we consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the manuscript has been substantially revised and expanded. Accordingly, we have also changed the manuscript titl

Production of ω\omega mesons in proton-proton collisions

The cross section for the production of $\omega$ mesons in proton-proton collisions has been measured in a previously unexplored region of incident energies. Cross sections were extracted at 92 MeV and 173 MeV excess energy, respectively. The angular distribution of the $\omega$ at $\epsilon$=173 MeV is strongly anisotropic, demonstrating the importance of partial waves beyond pure s-wave production at this energy.Comment: 12 pages, 4 figures submitted to Physics Letters B v2: figure 1 added, discussion detailing the data analysis, figure 3 (fig. 2 in v1) modified in line styles and systematic errors displayed on dat

Study of the p p -> p p pi+ pi- Reaction in the Low-Energy Tail of the Roper Resonance

Exclusive measurements of the p p -> p p pi+ pi- reaction have been carried out at Tp = 775 MeV at CELSIUS using the PROMICE/WASA setup. Together with data obtained at lower energy they point to a dominance of the Roper excitation in this process. From the observed interference of its decay routes N* -> N sigma and N* -> Delta pi -> N sigma their energy-dependent relative branching ratio is determined

Relativistic versus Nonrelativistic Optical Potentials in A(e,e'p)B Reactions

We investigate the role of relativistic and nonrelativistic optical potentials used in the analysis of ($e,e'p$) data. We find that the relativistic calculations produce smaller ($e,e'p$) cross sections even in the case in which both relativistic and nonrelativistic optical potentials fit equally well the elastic proton--nucleus scattering data. Compared to the nonrelativistic impulse approximation, this effect is due to a depletion in the nuclear interior of the relativistic nucleon current, which should be taken into account in the nonrelativistic treatment by a proper redefinition of the effective current operator.Comment: Added one new figure, the formalism section has been enlarged and the list of references updated. Added one appendix. This version will appear in Phys. Rev. C. Revtex 3.0, 6 figures (not included). Full postscript version of the file and figures available at http://www.nikhefk.nikhef.nl/projects/Theory/preprints

Comparison of Isoscalar Vector Meson Production Cross Sections in Proton-Proton Collisions

The reaction $pp\to pp\bf \omega$ was investigated with the TOF spectrometer, which is an external experiment at the accelerator COSY (Forschungszentrum J\"ulich, Germany). Total as well as differential cross sections were determined at an excess energy of $93 MeV$ ($p_{beam}=2950 MeV/c$). Using the total cross section of $(9.0\pm 0.7 \pm1.1) \mu b$ for the reaction $pp\to pp\omega$ determined here and existing data for the reaction $pp\to pp\bf \phi$, the ratio $\mathcal{R}_{\phi/\omega}=\sigma_\phi/\sigma_\omega$ turns out to be significantly larger than expected by the Okubo-Zweig-Iizuka (OZI) rule. The uncertainty of this ratio is considerably smaller than in previous determinations. The differential distributions show that the $\omega$ production is still dominated by S-wave production at this excess energy, however higher partial waves clearly contribute. A comparison of the measured angular distributions for $\omega$ production to published distributions for $\phi$ production at $83 MeV$ shows that the data are consistent with an identical production mechanism for both vector mesons

Donor states in modulation-doped Si/SiGe heterostructures

We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The results obtained from calculations for Si/Si$_{1-x}$Ge$_x$ quantum wells allow us to present the general behavior of the impurity states, as the donor position is varied from the center of the well to deep inside the barrier. The influence on the donor ground state from both the central-cell effect and the strain arising from the lattice mismatch is carefully considered.Comment: 17 pages, 10 figure

Fragmentation Function and Hadronic Production of the Heavy Supersymmetric Hadrons

The light top-squark \sto may be the lightest squark and its lifetime may be `long enough' in a kind of SUSY models which have not been ruled out yet experimentally, so colorless `supersymmetric hadrons (superhadrons)' (\sto \bar{q}) ($q$ is a quark except $t$-quark) may be formed as long as the light top-squark \sto can be produced. Fragmentation function of \sto to heavy `supersymmetric hadrons (superhadrons)' (\sto \bar{Q}) ($\bar{Q}=\bar{c}$ or $\bar{b}$) and the hadronic production of the superhadrons are investigated quantitatively. The fragmentation function is calculated precisely. Due to the difference in spin of the SUSY component, the asymptotic behavior of the fragmentation function is different from those of the existent ones. The fragmentation function is also applied to compute the production of heavy superhadrons at hadronic colliders Tevatron and LHC under the so-called fragmentation approach. The resultant cross-section for the heavy superhadrons is too small to observe at Tevatron, but great enough at LHC, even when all the relevant parameters in the SUSY models are taken within the favored region for the heavy superhadrons. The production of `light superhadrons' (\sto \bar{q}) ($q=u, d, s$) is also roughly estimated. It is pointed out that the production cross-sections of the light superhadrons (\sto \bar{q}) may be much greater than those of the heavy superhadrons, so that even at Tevatron the light superhadrons may be produced in great quantities.Comment: 20 pages, 9 figure