Solenoidal

The function (p is called the potential of an irrotational vector field and the function is called the potential of a solenoidal vector field. 

Braun and Hauck [3] discovered that the irrotational and solenoidal components of a 2-D vector field can be imaged separately using the transverse and longitudinal measurements, respectively. This result has a clear analogy in a 2-D tensor field. We can distinguish three types of measurements which determine potentials of the symmetric tensor field separately ... 

According to the Helmholtz theorem, the two-dimensional vector field can be represented as a sum of an irrotational field and of a solenoidal one... 

During the eontrol by Eddy Current, we exploit the information provided from a distance by impedance variation of a solenoid to the vicinity of a conductor material. 

It is the indication of a transfer of energy from a distance between the solenoid and the conductor material. The cause of the variation of impedance observed is the modification of the magnetic flow through the solenoid. The flow varies in amplitude and in phase. 

We propose a physical model, being based on the variation of the magnetic flow, allowing to determine defects characteristics. Some is the material and some is the geometry of the product, the presence of a defect allocates the flow in the straight section of the solenoid. The theoretical model proposed allows to find defects characteristics from the analysis of the impedance variation. 

The measure of the inductance variation observed during of the movement of the product in the solenoid generator allows to calculate directly the surface of the straight section of the defect of greater lengtli that the solenoid. More, tlie variation of the resistance allows to determine the height of the defect. 

Let us imagine a solenoid traversed by an alternating sinusoidal current near a conducting piece. The tension U on the coil is the sum of the tension Rsl due to the ohmic drop of potential in the coil of resistance Rs in the absence of eddy current and of the tension e opposing to the tension e given by the LENZS law ... 

L inductance of the solenoid in presence of eddy- current If we define the phases relative to the current then... 

These formulas are completely general and may be applied to any material, any form of piece and any coil. in the formula, the conductance is proportional to the amplitude of the part of the flux crossing the coil in phase with the current in the solenoid. 

A the time of eddy-current testing, we exploit information given at distance by the variation of the impedance [L,R] of a solenoid near a conducting piece to defect and characterize the defects. 

The variation of the Z of the solenoid mark a transfer of energy at distance between the solenoid and the conducting piece. The variation of the impedance is due to the modification of the magnetic flux d) crossing the solenoid. In fact, the flux differs in amplitude and in phase when the conducting piece is near the solenoid. Similarly, the flux will be influenced by the presence of defect. 

A physical theory about the effect of the eddy current on the impedance of the solenoid can be established by a simple way when we develop the fundamentals principles... 

In empty space a cylindrical sheet of current of any cross section and very longer than it s diameter, material by a long solenoid of length 1 with N single turn traversed by an current I. 

The effect of a long axial rectangular emerging defect of width e and of depth h is to increase the section Sa between the solenoid and the tube value of AS = eh. The induction in the space between the solenoid and the external surface of the tube and inside of tube remains unchanged. 

Where the indict D is noted when there is a defect, the indict Do is noted when there is no defect and the indict S is reserved to the empty solenoid. 

The experimental tests have validated the theoretical model for eylindrical products in non ferromagnetic material, therefore with a long solenoid ... 

The bulk magnetization is stimulated into processional motion around Bq by a radiofrequency (RF) pulse at Vj, applied tlirough a solenoid-like coil whose axis is perpendicular to Bq. This motion amounts to a nuclear... 

Figure Bl.12.4. Construction of a high-field superconducting solenoid magnet.

The question is if in reality such magnebc fields exist. It turns out that such fields can be fonned by long and narrow solenoids [11 lb]. It is well known that in this case the magnetic fields are nonzero only inside the solenoid but zero... 

When the curvature of the reaction vessel is too great for the efficient operation of the bar type magnetic stirrer, a miniature solenoid-operated reciprocating stirrer may be employed (Fig. XII, 2, 19). This stirrer may be easilj constructed from a telephone relay or electric bell. It is advisable to have a control for adjusting the stroke while running. 

Titrations may be automated using a pump to deliver the titrant at a constant flow rate, and a solenoid valve to control the flow (Figure 9.5). The volume of titrant delivered is determined by multiplying the flow rate by the elapsed time. Automated titrations offer the additional advantage of using a microcomputer for data storage and analysis. 

A more advanced mirror approach involving multicells, called the tandem mirror, has been studied as a means to overcome the leakage problem. One way to view the tandem mirror is as a long uniform magnetic solenoid with two single-cell mirrors installed at the ends to electrostatically plug the device. Plasma end losses ate impeded by electrostatic potentials developed by the plasma as the electrons and ions attempt to leave the device at different rates. 

Fig. 22. Superconducting magnet configurations for MHD generators where the arrows represent the magnetic lines of force, (a) Solenoid (b) racetrack ...

---