Coupling loops

To construct the pertraction network, the particular reaction networks should be added via 0 junctions to three linear networks corresponding with the processes of diffusion of C2A, C2B, and CH carrier species. The resulting reaction-diffusion network, as presented in Figure 13.6, consists of four coupled loops representing the pertraction of A " ", and H" " cations. The loops are coupled by common capacitances Aj, Bj, and Hj (i = f, s) and by the capacitances CHj and CH for a reacting or diffusing acidic form of the carrier. From the network in Figure 13.6, all the model equations used further in numerical calculations can be deduced with the help of Kirchhoff s law for a 0 junction (KCL) ... 

Fig. 103. Capacitively coupled microwave plasma (A) [442] and microwave induced plasma discharges (B, C). (B) MIP in a TMoio resonator according to Beenakker (a) cylindrical wall, (b) fixed bottom, (c) removable lid, (d) discharge tube, (e) holder, (f) coupling loop, (g) PTFE insulator, (h) ...

The reaction-diffusion network, as presented in Fig. 5.5, consists of four coupled loops representing the pertraction of A-+, B2+, and H+ cations. All model equations used further in numerical calculations can be deduced with the help ofKirchhotTs law for a 0 junction (KCL) ... 

Rgure 1 A TMqio tyP resonant cavity. The position of the coupling loop and the viewing and cooling ports are shown. The discharge tube is centered in the holes at the top and bottom faces of the cavity. (Matousek JP, Orr BJ, and Selby M (1984) Microwave-induced plasmas Implementation and application. Reviews in Analytical Atomic Spectroscopy 7 275-314.)... 

The cross-sectional area under the coupling loop, compared to the cross-sectional area of the cavity (see Fig. 5.77). This effect can be compared to the turns ratio principle of a transformer. 

The orientation of the coupling loop to the axis of the magnetic field Coupling from the cavity is proportional to the cosine of the angle at which the coupling loop is rotated away from the axis of the magnetic field, as illustrated in Fig. 5.78. 

FIGURE 5.78 Top view of a cavity showing the inductive coupling loop rotated away from the axis of the magnetic field of the cavity. 

There are several ways to design a notch hlter, but they aU accomplish the same purpose. In one form, a notch filter is a bandpass cavity with only an input coupling loop, mounted off the transmission Hne by means of a matched tee. Other designs employ some form of capacitive coupling of the tuned frequency into a cavity and away from the main transmission Hne. 

The inductive method uses seawater as the coupling loop between two transformers (Ti and T2 in Fig. 3-2b). Through this loop, the transformer Ti induces a current in T2 which is measured with a galvanometer (G in Fig. 3-2b). The induced current depends on the coupling in the compensating loop with resistor Rp. This loop induces a coimter current in T2. If Rp is changed such that the current through G vanishes, R Rp. 

But if a measurement is used to decouple fully coupled loops, a positive feedback path is formed through the process, cancelling the effect of control action. As a result, the system has no direction and the controlled variable tends to float. Measurements may be used in systems with half-coupled loops, however, because there is no feedback from one loop to another through the process. 

Half coupled loops such as the one shown in Fig. 7.5 are simple to decouple, and little risk is involved. The decoupling is in one direction only, and there is no possibility of a positive feedback loop. Therefore a measurement of the independent controlled variable can be used to decouple the output of the dependent loop. 

This is a matrix of open loop gains whose actual values have not been inserted. The intent is to show that half-coupling exists between Q, p, and T. But normalization according to the procedure outlined in Chap. 7 yields a unit diagonal, with all other elements zero. This proves the absence of full coupling, and makes pairing obvious. The detailed equa tions for decoupling of the half-coupled loops follow. 

This device is in principle a classical double-gap buncher with a travel time of 10 ns for the positrons through the drift tube. When compared to a A/4 coaxial resonator, the double-gap resonator is preferable because of the shorter length and the lower rf power consumption resulting from two bunching gaps. The rf power is fed in by a coupling loop and a pick-up loop is used for control and regulation pur-... 

In general, the major system-analysis codes are equipped to model all of the equipment components and associated physical phenomena and processes that are expected to occur. The codes and modeled namral-circulation and parallel-channel flows for the coupled NCL case require validation by comparisons of predictions with experimental data. The major codes, the several locally developed special-purpose models and codes, and application procedures have been validated by use of many of the simple pure thermal-hydro experiments and analytical results for NCLs and parallel-channel flows. However, in general, the general-purpose major codes must be validated for applications to complete coupled-loop systems for design, development of deep understanding, and safety-grade analyses. 

The few investigations into the properties and characteristics of coupled NCLs include Salazar et al. (1988) for idealized coupled loops with specified energy input and extraction over the primary and secondary loops, respectively. Wu (2011) has analyzed the case of a general number of coupled loops following the idealized approach of Welander. The mathematical model reduces to a system of coupled ordinary differential equations (ODEs) analogous to a coupled system of the equations developed by Lorenz (1963). 

The modeling is based on adaptation of the equations in the previous section to the coupled loops case. The model equations developed herein will be written for the case of single-phase flow in the primary and secondary loops. Both steady-state and off-normal transient conditions in the Gen IV nuclear reactor case involve two-phase fluid states. Safety-grade analyses of design and off-normal states will generally be handled by systems-analysis models and codes that easily accommodate generalized geometry, fluid states, and flow directions. 

The BCs for the equation system, in the general case considered in Fig. 16.4, are given by the inlet temperature at the hot end of the energy supply HEX, Tjun, and the inlet temperature at the cold end of the energy sink HEX, Fein. In the general case, these BCs can be taken to be functions of time to allow introductions of perturbations in the BCs. The steady-state performance of the coupled loops is determined by... 

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