Dear Referee
Thank you for reviewing our paper. Since we wanted to obtain our simulation
results plus comparing it with experimental results, it took about three months to
prepare response. Now we have calculated the problem numerically using a finite
element code. Other side, we have compared our results with very famous result done
by Karney and Fisch (C. F. F. Karney and N. J. Fisch, Phys. Fluids 29(1), 180
(1986)). It seems the result is sufficient about proving of the suitability and validity of
our paper. Here, we have presented some results of our numerical work related to the
next paper that we will submit it in next step (we had already mentioned about this
next step in the first paragraph of the page 3 of the article) in near furture.
About comments of the referee:
1) The referee believes: they base the calculation on a local analysis of the
Fokker-Planck equation and the effect they look at is certainly not an
inductance in any generally accepted sense of the term. Inductance describes
the effect of driving up magnetic field and depends on the geometry of the
complete circuit.
In response we say that is correct and the inductance introduced in the article
is not generally considered by others but that is a real inductance property that
can be confirmed theoretically and experimentally. Generally inductance
describes the effect of driving up magnetic field and it usually depends on the
geometry of the complete circuit. This effect of driving up magnetic field
appears when an electric charge (for example electron) accelerates or
decelerates. Usually this accelerating or decelerating is due to the geometry of
the complete circuit, but it can be also caused by a distortion in electron
distribution function that appears in RF-wave heated plasmas. This effect can
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be considered as the flux crossing the surface of critical energy mv ph 2 in
the velocity space, resulting in a large rate of change of high-energy current
carries. This new effect of inductance can be compared with intrinsic concept
of curvature that appears in the General Relativity theory related to gravity. As
a remind: a curve on a surface has curvature for two reasons. First, if the
surface itself is curved, and bends relative to the surrounding 3-dimensional
space that contains it. This type of curvature is essentially related to the
intrinsic of the surface. Second, whether the surface is curved or not, the curve
may curve within or relative to the surface. In inductance property, a driving
up magnetic field may be caused by the geometry of the complete circuit or a
distortion in the velocity space. Here in our article a new inductance meaning
is introduced that depends on the intrinsic concept of the velocity space. We
think this concept is very important and it can change the meaning of the
inductance in physics and engineering. It seems this new effect has not been
considered by others.
2) The referee believes: …The authors state explicitly that any change in the
steady field is over a time scale long compared to the collision time.
This comment is due to the relation (18) and state after this formula (“where
we have assumed the electric field is dc and changes much smaller than the
time collision”) in old version. The reason of that statement was because we
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wanted to integrate Eq. (8). In that integration we tried to take out the electric
field under the integral sign to get a simple relation (equation 18 in old
version). But here in the revised version we have eliminated that method and
in result we have changed the Eqs. (18) and (21). With these changes any
problem related to “change of steady field is over a time scale long compared
to the collision time” will be eliminated.
In proof of validity of our calculation, we present here our numerical
calculation (that will be appeared in next article).
In Fig. 1 the characteristic of induced inductance L versus E for Z  1 in
lower-hybrid heating of plasma is shown. For convenience we have plotted
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a 2 e 2 v ph Pd R0 m 2  .L versus v ph q m  .E instead of L versus E . This
figure is obtained from solution of Eq. (6) using a finite element code and it is
compared with the linear case calculated in our article (equation 21). It is
evident from the figure, the line will locate in the curve in the limit of E0
that shows our theoretical calculation in the article is absolutely true.
Other side, as mentioned in the article this induced inductance can affect on
the efficiency of RF-wave heated plasmas. The efficiency of RF-wave heated
plasmas has been already calculated by Karney and Fisch (C. F. F. Karney and
N. J. Fisch, Phys. Fluids 29(1), 180 (1986)) without considering the induced
inductance property. In Fig. 2 we have estimated this efficiency for lowerhybrid-wave heated plasmas with considering the induced inductance
property. We have compared it with Karney and Fisch theory together the
experimental results from the PLT facility (C.F. F. Karney et al, Phys. Rev., A
32, 2554 (1985)). These comparisons confirm strongly our theoretical
results obtained in the article.




2
Fig. 1.
z=1
10
0
2 2
ph d
0
2
(a e v P /R m .L
5
-5
-10
-15
-8
-6
-4
-2
(v
0
2
4
2
ph
q/m.E
Fig. 1. The characteristic of induced inductance of lower-hybrid current drive versus
electric field for Z=1. The red line shows the linear case obtained from the article in
relation (21), the black curve shows the nonlinear case obtained from solution of Eq.
(6) using a finite element code.
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Fig. 2. Comparison of experimental data obtained from PLT (curve 3) with
considering the induced inductance effect on the efficiency (curve 1)
obtained from our paper and without considering the induced inductance
effect on the efficiency (curve 2) obtained by Karney and Fisch. These are
for lower-hybrid-wave-heated plasmas in case of Z=5.
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Fig. 3. Experimental results of efficiency of lower-hybrid-wave-heated plasma in PLT
obtained from C.F. F. Karney et al, Phys. Rev., A 32, 2554 (1985). We have used this
plot in Fig. 2.
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