<br /><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2"><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Replying to:</font></span><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"><font size="2">As always you have distorted what I said and are attacking what you wish I had said. What I said is that circuit theory is a low frequency lumped parameter approximation to Maxwell's equations that can be applied only under certain circumstances. <br />Posted by DrRocket</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Replying to:</font></span><font size="2"><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">I.5. </span><strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">Boundary Conditions. Circuit Dependence</span></strong></font><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"><br /><font size="2">In applying the classical theory and its modem development, the importance of boundary conditions has often been neglected . As a result, infmite plasma models, or models with static boundary conditions, are often applied to problems with variable boundary conditions. This gives completely erroneous results (examples are given in III).<br />In many theories, it is taken for granted that the behaviour of a plasma depends only on the local parameters (e .g ., density, temperature, magnetic field) . This can be quite misleading </font></span><font size="2"><strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">. As an example, in a non-curlfree (<u>i .e ., current carrying</u>) plasma, the properties of the plasma are not only a function of the local parameters, but also of the outer circuit in which the current I closes (1I .5).</span></strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"></span></font><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">That seemed to be news to you. The circuit energy is critically important in such events DrRocket, not just the local conditions in the plasma.</DIV></font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Once again you have focused on semantics and terminology and have completely distorted the physics and what it is that Alfven has said.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Alfven is quite correct in his concern over proper application of boundary conditions to a distributed parameter problem described by Maxwell’s set of partial differential equations.<span> </span>He is absolutely correct in objecting to static boundary conditions being applied to a dynamic situation.<span> </span>His example, one in which the Maxwell-Faraday equation relating the curl of the E field to the time variation in the B field requires an adequate model.<span> </span>In the non-curlfree situation one applies Stokes theorem and finds that the E field is non-conservative and that an electromotive force exists around closed loops.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Having correctly notices that the situation described by Maxwell’s equations provides for an electromotive force, Alfven uses a model, called an <strong>equivalent circuit</strong> to aid in describing the complex phenomena that are properly described by Maxwell[‘s equations.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">There is nothing wrong with the technique of using an equivalent circuit, once the underlying physics has been properly described by the proper partial differential equations and once necessary approximations have been justified and made to produce the equivalent circuit. <span> </span>The equivalent circuit, being described by ordinary differential equations is easier to solve and provides a useful bit of intuition to someone adept at circuit analysis. <span> </span>But an equivalent circuit is not a physical circuit, and Alfven is not directly applying circuit theory to the plasma, which would be inappropriate without first looking at the problem using more exact methods of field theory.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Replying to:</font></span><font size="2"><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">Figure II .16 shows a simple circuit consisting of an electromotive force Vb , a resistor Ro, and an inductance L . By changing R 0 and/or L, the behavior of the plasma may be changed in a drastic way . The value of Ro decides whether the plasma is relatively stable or oscillating . If the plasma contains a double layer which explodes, the circuit energy iLI2 is released in the layer .</span><strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"> Hence, the violence of the plasma explosion is determined largely by the circuit</span></strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">. </span><strong><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'">The influence of the `circuit' is essential, not only in a laboratory experiment, but also in space</span></strong></font><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"><font size="2"> . In the latter case, the total volume in which the current flows affects the<br />behavior of the plasma at every point . In many instances, it is convenient to introduce the boundary conditions by drawing an `equivalent circuit' (II and III).</DIV></font></span><span style="font-size:9.5pt;font-family:'Verdana','sans-serif'"><font size="2"> </font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">The emphasis here is yours; notice that Alfven has put the word “circuit” in quotes.<span> </span>And note the last sentence in which he very specifically tells the reader that the circuit in question is an EQUIVALENT CIRCUIT.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Equivalent circuits are a rather standard commodity in electrical engineering.<span> </span>In circuit theory itself once find Thevenin’s and Norton’s equivalent circuits used.<span> </span>In that case the purpose is the reduction of a complex circuit to one involving only a voltage source and a single series impedance (Thevenin) or a current source and a single parallel impedance (Norton).<span> </span>They represent the input-output characteristics of the original linear circuit faithfully, but one loses all information regarding anything that is internal to the circuit.<span> </span>In the theory of machinery one also finds equivalent circuits used to describe the operation of things like motors.<span> </span>Again those circuits are useful tools in describing some aspects of the operation of the machine, but they are limited in application to only some aspects of that operation.<span> </span>Is should be pretty clear that a circuit composed of resistors, capacitors and inductors is not a real motor.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Equivalent circuits are useful models, once the underlying physics has been described by the appropriate partial differential equations of field theory.<span> </span>Only then can valid approximations be made and the resulting equations reduced to analogs in the form of equivalent circuits.<span> </span>The advantage of the equivalent circuit is that one can then apply the intuition that one has from solving circuit equations as a device to help in understanding the more precise and correct formulation of field theory an partial differential equations, but having only to deal with lumped parameter models and ordinary differential equations.<span> </span>This approach is sometimes taken to study the systems of masses, springs and dashpots, studied by mechanical engineers, representing them as ordinary RLC circuits, and in fact building circuit analogs to study those mechanical systems.<span> </span></font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">In the case of plasmas, what Alfven has done is to apply the full machinery of field theory and his insight into plasmas to construct equivalent circuits to help describe some aspects of the behavior of the plasma.<span> </span>He has not directly applied circuit theory to the plasma, but has constructed a simplified model based on some approximations.<span> </span>The circuit here is not simply some structure that he finds in the plasma itself, but is based on field theory and approximations to it.<span> </span>Properly applied the insight provided is no doubt valuable.<span> </span>Alfven is applying the physics properly.<span> </span>You are interpreting that application improperly.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Given your predilection for abusing terminology and semantics a word regarding the notion of an equivalent circuit is in order.<span> </span>An equivalent circuit in electrical engineering has a rather specific technical meaning.<span> </span>It is equivalent only with regard to certain characteristics.<span> </span>Normally that means that input-output characteristics of the circuit are a good model for the parent phenomena.<span> </span>Thevinin and Norton equivalent circuits are good models downstream of the terminals of the circuit, but internal parameters are irrelevant to the real physics.<span> </span>Equivalent circuits of motors are constructed so that, for instance, the energy dissipated in the resistor is the work performed by the motor.<span> </span>But the equivalent circuit is not the real phenomena the analogy holds only insofar as the circuit is constructed to reflect specific and targeted aspects of those phenomena.<span> </span>The equivalence is not universal.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Get over yourself. You aren't more of a "circuit" expert an how it relates to plasma physics than Hannes Alfven. He certainly understood the boundary conditions and where it would be useful to look at the local plasma conditions and where it would not be useful to look at the energy coming from the whole "circuit". The fact you're still debating this point shows how irrational you've become. There is no doubt that "circuits" can be applied to plasma physics and that Alfven himself applied circuit theory to plasma physics. All the math you'll ever want or desire is in that book and in the work of Anthony Peratt, but of course you're evidently smarter than everyone on circuit theory as it relates to MHD theory, including Alfven, Peratt, Scott and all of their students.</DIV></font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">So once again, we see that you have distorted the words of Alfven and are again focusing on semantics at the expense of physics.<span> </span>Alfven is not applying circuit theory to plasma physics, but is simply constructing a useful analogy in the form of an equivalent circuit.<span> </span>That construction can and does provide useful insight, but it in no way replaces the need to understand the fundamental nature of the problem which is properly described by a lumped parameter and partial differential equations.<span> </span>Circuit theory is, as I have told you, only a lumped parameter low-frequency approximation to the field theory of Maxwell’s equations, and application of that theory requires first an understanding of what is going on at the field theory level.</font></span><span style="font-size:12.5pt;font-family:'Verdana','sans-serif'"><font size="2">Equivalent circuits are limited but useful tool.<span> </span>It is important to understand the limitations.<span> </span>The technique and the limitations are widely understood and applied in electrical engineering.<span> </span>If you had not dropped out of that curriculum you might understand that too.</font></span> <div class="Discussion_UserSignature"> </div>