J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Bessel Function Model of the Electron Pressure Profile Normalized by
Gyro-Bohm Type Parameter Dependence
Junichi MIYAZAWA, Tomohiro MORISAKI, Motoshi GOTO, Ryuichi SAKAMOTO,
Gen MOTOJIMA, Masahiro KOBAYASHI, Kiyomasa WATANABE, Hisamichi FUNABA,
Ichihiro YAMADA, Kenji TANAKA, Akiyoshi MURAKAMI, Hiroshi YAMADA,
and LHD Experiment Group
National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, Japan(Received: 4 November 2009 / Accepted: 8 March 2010)

A model of electron pressure profile named gyro-Bohm normalized Bessel function model (GB-BFM) has been
proposed. GB-BFM is composed of a profile term given by zero-order Bessel function, which is based on the
diffusive transport in cylindrical plasmas, and gyro-Bohm type parameter dependences on the density profile, thetotal heating power, and the magnetic field strength. Using GB-BFM, one can figure out the region where thetransport is gyro-Bohm like and diffusive. GB-BFM has been applied to the experiments in LHD. Profile analysisof the plasmas with or without a large magnetic island induced by resonant magnetic perturbation coils has revealed
that the gyro-Bohm like diffusion is prevailing in the plasmas independent of the existence of island, except for theedge region. The gyro-Bohm like and diffusive transport property is also recognized in the mantle region ofhigh-density plasmas with an internal diffusion barrier, while the superdense core region is improved comparedwith GB-BFM.
Keywords: heliotron, energy confinement scaling, RMP, magnetic island, high-density, IDB, mantle
observed [7-9], although the possible existence of a criticalgradient has been suggested in W7-AS [6]. Therefore, a
new kind of scaling law including the profile terms ishighly desired especially for helical plasmas. Of course, it
is desirable that this new scaling can also describe tokamak
plasmas,forcomprehensive
understandingsofmagnetically confined plasmas.
In this study, a model of electron pressure profile incylindrical plasmas is considered as a first step to construct
a new scaling consisting of the profile terms. Details of themodel are described in the next section. This model is thenapplied to the experiments in LHD [10]. Two kinds ofneutral beam (NB) heated plasmas are chosen as typicalexamples; one is the plasma with a large magnetic island
induced by resonant magnetic perturbation (RMP) coils[11,12] and another is the plasma with internal diffusion
barrier (IDB) formed after intense hydrogen ice-pellet
injection [13-15], which are described in Sections 3 and 4,
respectively. Finally, a summary is given in Section 5.

1. Introduction

Energy confinement times, τE, in magneticallyconfined plasmas have been intensively studied for many
years. This time constant describes the conductive loss
from the plasma as PL = Wp/τE, where Wp is the plasma
stored energy that is proportional to both the density andtemperature. In a fusion device, the sum of PL andradiation loss is compensated by the heating power. It istherefore important to investigate the physics that
determines τE, to predict the power balance in a future
fusion reactor. Scaling laws of τE have been empiricallyderived. H-mode scalings for tokamaks [1,2] andinternational stellarator scalings (ISS) for helical plasmas[3,4] are the typical examples. These scalings usuallyconsist of both device parameters and operationalparameters. Once the operational conditions including theheating power and averaged-density are given, these
scalings can predict Wp and therefore the averagedtemperature in a device.
In a fusion reactor driven by alpha heating, however,the local temperature in the core region is more important
than the averaged-temperature, since the thermo-nuclear
fusion reaction mainly occurs in the high-temperature coreregion. As long as the radial profile of the temperature is
known, as observed as stiffness in tokamaks [5,6], it isstraightforward to estimate the core temperature from theaveraged-temperature. However, this is not the case inhelical plasmas where no strong stiffness has been

2. Gyro-Bohm Normalized Bessel Function Model

2-1. Gyro-Bohm model
ISS95 [3] has been often referred to as a standard of
the global energy confinement time in helical plasma
experiments. This has been updated to ISS04 with newdata from LHD and other devices [4]. ISS04 is called agyro-Bohm like scaling, since its non-dimensional form isapproximately proportional to τBohm/ρ*, where τBohm is theauthor’s e-mail: miyazawa@LHD.nifs.ac.jp

94©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

J. Miyazawa et al., Bessel Function Model of the Electron Pressure Profile Normalized by Gyro-Bohm Type Parameter Dependence

Bohm confinement time and ρ* = ρi/a is the ion
gyro-radius normalized to the plasma minor radius. Similar
gyro-Bohm like dependence is also recognized in ISS95
and tokamak H-mode scalings [7]. The gyro-Bohm modelis based on the drift-turbulence models, where the micro
turbulence that drives anomalous transport has a scale
length of the order of ρi with a decorrelation time of theorder of ion diamagnetic drift time [16-19]. The thermal
diffusivity in the gyro-Bohm model is given by χGB ∝ T 1.5/ (a B2), where T is the temperature and B is the magnetic
field strength. Using a relation of Wp ∝ a2 R ne T ∝ PH τE(i.e., T ∝ PH τE a –2 R –1 ne –1), the pure gyro-Bohm scaling,τGB ∝ a2 / χGB ∝ a3 B2 T –1.5 ∝ a3 B2 (PH τE a –2 R –1 ne –1) –1.5
(i.e., τGB2.5 ∝ a6 R1.5 PH–1.5 ne 1.5 B2), is given byτGB ∝ a2.4 R0.6 PH–0.6 ne 0.6 B0.8,

diffusive. Also note that the steady-state solution with aheating profile proportional to ε(ρ), i.e., PH(ρ) ∝ ε(ρ) ∝J0(2.4 ρ), also has a radial profile proportional to J0.
2-3. Gyro-Bohm normalized Bessel function model
According to the discussion above, the pressure
profile in cylindrical plasmas, or high-aspect ratio toroidal
plasmas, is proportional to J0, as long as the transportcoefficient is independent of ρ. Assuming the gyro-Bohm
type parameter dependence as in Eq. (1) and constantelectron density of ne(ρ) = n, the electron pressure profile,pe(ρ) (∝τGB PH) can be modeled bype(ρ) = C n0.6 PH0.4 B0.8 J0(2.4ρ),(1)

where C is a constant. In the experiments, however, thedensity profile is not a constant. To include this effect, we
assume that the local electron pressure at ρ = ρ1 isexpressed by substituting the local electron density ne(ρ1)
for n, i.e.,

where R, PH, and ne denote the plasma major radius, theheating power, and the line-averaged electron density,
respectively.

pe(ρ1) = C ne(ρ1)0.6 PH0.4 B0.8 J0(2.4ρ1).

2-2. Bessel function model
Here, let us consider a model of energy profile, ε(ρ),
where ρ is the normalized minor radius defined by thesquare-root of the toroidal flux normalized so as to give ρ= 1 at the last-closed-flux-surface (LCFS), in cylindricalplasma as an approximation of high-aspect ratio toroidal
plasma. Volume integration of ε(ρ) gives Wp (i.e.,∫01ε(ρ)(dV/dρ)dρ = Wp). Note that ε(ρ) is proportional tothe pressure profile that is the product of density andtemperature, i.e., ε(ρ) ∝ p(ρ) ∝ n(ρ) T(ρ). Assume that ε(ρ)
self-similarly decays with a time constant of τ, i.e., ε(ρ, t) =ε(ρ) exp(–t/τ). The energy flux is given by Γ = – χ ∇ε,where the diffusivity χ is assumed to be independent of ρ.
It should be noted that the Γ in this model is composed ofthe energy fluxes driven by both the temperature anddensity gradients. Therefore, the χ here does notnecessarily equal to the conventional thermal diffusivity,
which is related to the temperature gradient alone. The
continuity equation is given by ∂ε/∂t = – ∇⋅Γ, that can betransformed to (–1/τ ) ε(ρ) = χ ∇2 Γ, and1 ∂ ⎛ ∂ε ⎞
1
⎜⎜ r
⎟⎟ +
ε = 0.
r ∂r ⎝ ∂r ⎠ χτ

(5)

Extending this to the whole radial position, we define thegyro-Bohm normalized Bessel function model (GB-BFM)
of pressure profile, pGB-BFM(ρ) as below;
pGB-BFM(ρ) = C ne(ρ)0.6 PH0.4 B0.8 J0(2.4ρ/α),(6)where α = aJ0=0/aLCFS is introduced to explicitly include theexperimental observation that the radial position, aJ0=0,
where the pressure becomes zero is ordinarily different

normal discharge (gas fueled)10.8#87564, t = 2.7 s

p / (n
e

0.6
e

P

0.4
H

0.8

B )

0.6
0.4
C J (2.4ρ/α)

0.2

(2)

0

The solution of Eq. (2) is given by zero-order Bessel
function, J0, as below;

0(C = 0.66, α = 1.28)
-1

-0.5

0

ρ

0.5

1

Fig.1 Typical radial profile of gyro-Bohm normalized
electron pressure in a density ramp up discharge
fueled by gas puffing (see Figs. 2 and 4). The
result of least-square fitting to zero-order Bessel
function is also shown. In the shaded region, theelectron pressure profile is well reproduced by
GB-BFM.

ε(ρ, t) = ε0 J0(r/(χτ)0.5) exp(–t/τ),= ε0 J0(2.4 ρ) exp(–t/τ),

(4)

(3)

where ε0 is the central value of the energy profile that will
be determined by the experiment. Note that no convection
is assumed in this model and therefore the transport is fully95

J. Miyazawa et al., Bessel Function Model of the Electron Pressure Profile Normalized by Gyro-Bohm Type Parameter Dependence

NB heating power, PNB. Nevertheless, the central electron
density, ne0, and pressure, pe0, are similar for these twodischarges.
According to the gyro-Bohm model, or theinternational stellarator scalings, Wp = PH τE is expected to
be proportional to ne 0.6 (see Eq. (1)). This relation is also
recognized in the experiment. In Fig. 3(left), Wp in four

from the radial position of LCFS, aLCFS.
In the following sections, we use PGB-BFM(ρ) to fit theelectron pressure profiles measured by Thomson scattering[20]. The constants C and α are determined by theleast-square method to fit the pressure data at 0 < ρ < ρmax
to the model, where ρmax is also optimized to give theminimum of chi-square. The equilibrium used for data
mapping, which is chosen from a database calculated by
VMEC code [21], is also optimized in the fitting procedure.
In some cases, we will compare the gyro-Bohm
normalized pressure profile, pe(ρ)/(ne(ρ)0.6 PH0.4 B0.8), andC J0(2.4ρ/α), instead of comparing pe(ρ) and PGB-BFM(ρ). A
typical example of fitting result is shown in Fig. 1, where
the gyro-Bohm normalized electron pressure profile in adensity ramp-up discharge fueled by gas puffing iscompared with the best fit of C J0(2.4ρ/α). This discharge
will be discussed again in the next section. As is seen in the
figure, our model can fit the electron pressure profile insideρ ~ 0.9. In other words, the transport in this region is
gyro-Bohm like and diffusive. In the edge region of ρ ~ 1,
however, our model fails to reproduce the steep pressure
gradient, i.e., the transport in this region is non-gyro-Bohm
and/or non-diffusive. This region is enlarged in the plasmas
with a large magnetic island, as will be shown in the next
section.

(a)
(b)

H

e0

4
p

e0

(d)

10
1.5

2.5
time (s)P ~ 14 MW

3

3.5

0.6

y = 4.2 x

H

y = 140 x#87564#8756415#875522

Fig.2 Waveforms in density ramp-up discharges
fueled by gas puffing with (#87559, brokenlines or closed circles) or without (#87564,
solid lines or open squares) a large m/n = 1/1
magnetic island. (a) The diamagnetic plasma
stored energy, Wp, (b) the NB heating power,
PH (and the radiation loss, Prad), (c) the central
electron density, ne0, and (d) the central
electron pressure, pe0, are shown.

20"w/o island"#875520.6

y = 90 x"w/o island"

P

n

0
20

"w/o island"

10

300

#87559"with island"

200#87559#87553

100
0

P

8

(c)

"w/o island"

400

w/o island(#87564)pwith island (#87559)

0
12

0.6

H

500

W

0

P ~ 14 MW

0rad

In LHD, a large m/n = 1/1 and/or 2/1 magnetic island
can be formed using RMP coils, where m and n denote thepoloidal and toroidal mode number, respectively.
Especially, the large m/n = 1/1 island formed in the edge
region influences the global confinement. Typical density
ramp-up discharges with (#87564) or without (#87559) alarge m/n = 1/1 island are compared in Fig. 2. The RMP
coils were activated throughout the discharge duration in#87559. The diamagnetic plasma stored energy, Wp, islargely reduced in the discharge with the island (#87559),
compared with the normal discharge (#87564) at similar

600

ax

10

3. Impact of the Magnetic Island

700

R = 3.85 m, B = 2.57 T

800
600
400
200
0

"with island"

0

2

4

6

8

19

-3

n (10
e

5

"with island"

10#87553"with island"

0

12

m )

0

2

4

6

8

n

19

-3

e0

(10

10

12

m )

Fig.3 (left) The plasma stored energy dependence on the line-averaged electron density, and (right) the central
electron pressure dependence on the central electron density, in discharges with or without the island.

96

J. Miyazawa et al., Bessel Function Model of the Electron Pressure Profile Normalized by Gyro-Bohm Type Parameter Dependence

normal discharge (w/o island)with m/n = 1/1 island#87564: R = 3.85 m, B = 2.57 T, P ~ 14 MW#87559: R = 3.85 m, B = 2.57 T, P ~ 14 MW

H

(a1)

2 T

e

1
0

(b1)

10
0

(c1)

10
0

(d1)
(e1)

1

t = 2.7 s

1

H

(a2)

2 T

e

(b2)

e

10
0

p

e

(c2)

-1

(d2)

GB-BFM

-0.5

(e2)
0

ρ

0.5

10

t = 2.7 s

e

p

e

0.6

1 pe / (ne

0.4
0.8
B )
H
0

P

0
2 p /p
1
0

1

Flat

n

0

0.6
0.4 0.8
p / (n
P
B )
e
e
H

e

t = 1.5 s
t = 2.0 s

1
0

n

0
2 p /p0

Fig.4

t = 1.5 s
t = 2.0 se

GB-BFM

-1

-0.5

0

ρ

0.5

1

Radial profiles of (a1/a2) the electron temperature, (b1/b2) the electron density, (c1/c2) the electron pressure,(d1/d2) the gyro-Bohm normalized electron pressure, pe(ρ)/(ne(ρ)0.6 PH0.4 B0.8), and (e1/e2) the ratio of pe(ρ) to
the fitting result of pGB-BFM(ρ), in the normal discharge without island (#87654, left column) and the discharge
with the island (#87559, right column). In the shaded regions, the pe profiles are well reproduced by the
GB-BFM.
(ρ = 1). The density profile is hollow and its peak locatesaround ρ ~ 0.9. The density gradient at 0.9 < ρ < 1.0
suggests an existence of inward particle convection, since
the temperature in this region is so high (200 – 600 eV)that the particle source due to the ionization of light ion
species is negligible.
In the discharge with the m/n = 1/1 magnetic island(right column in Fig. 4), on the other hand, flattening of thetemperature profile due to the island is recognized in theedge region of ρ ~ 1, where the ι = 1 surface exists in thismagnetic configuration (ι = ι/(2π) =1/q is the rotationaltransform and q is the safety factor). The edge density
decreases in this case. The magnetic island is intersecting
the LCFS and therefore connecting the confinement region
and the region outside the LFCS called stochastic layer.
Although the mechanism is not fully understood yet, thisconfiguration enhances the particle transport in the edge
region. The density peak observed at ρ ~ 0.9 in the normal
discharge moves to ρ ~ 0.7 – 0.8 in the discharge with theisland. The pressure profile shrinks due to the island,
although the achieved central pressure is similar to that in
the case without island. This shrinkage of pressure profile
directly causes degradation in the global confinement.
The gyro-Bohm normalized pressure profile alsoshrinks due to the island. Nevertheless, the central value of
this normalized pressure is not influenced by the existencedischarges with or without the island are plotted withrespect to ne . In the normal discharges without island, Wp
is proportional to ne 0.6. Similar density dependence is also
recognized in the discharges with the island, although theproportional coefficient decreases from 140 to 90. As will
be discussed later on, this confinement degradation can be
attributed to the shrinkage of confinement region due to thelarge island. Even though the global confinement isdegraded, the central pressure is not influenced by theisland as shown in Fig. 3(right), where pe0 in the samedischarges as shown in Fig. 3(left) is plotted with respect tone0. In this case, pe0 in these four discharges shows similar
density dependence of pe0 ~ 4.3 ne00.6, i.e., the gyro-Bohm
like density dependence is also recognized in the relation
between the local central electron pressure and the local
central electron density.
As seen in Fig. 3, both the plasma stored energy andcentral pressure show gyro-Bohm like density dependence,
while the response to the large magnetic island is different.
To explain this, radial profiles of the electron temperature,density, and pressure are compared in Fig. 4, together withthe gyro-Bohm normalized pressure profile ofpe(ρ)/(ne(ρ)0.6 PH0.4 B0.8) and the ratio of pe(ρ) to the fitting
result of pGB-BFM(ρ) introduced in Section 2. In the normal
discharge without island (left column in Fig. 4), thetemperature profile is expanding slightly outside the LCFS

97

J. Miyazawa et al., Bessel Function Model of the Electron Pressure Profile Normalized by Gyro-Bohm Type Parameter Dependenceof the island. This is expected from the result shown in Fig.
3(right), where the gyro-Bohm like density dependence ofthe central pressure appears to be common for thedischarges with and without the island. The region where
this gyro-Bohm property is prevailing and the transport isdiffusive is clearly shown in the bottom panels of Fig. 4,
where radial profiles of the ratio of pe(ρ)/pGB-BFM(ρ) are
shown. The ratio is ~ 1, and therefore the transport isgyro-Bohm like and diffusive, at ρ < 0.9 in the normal
discharge, and at ρ < 0.7 – 0.8 in the discharge with theisland.
Summarizing, the magnetic island causes shrinkage ofpressure profile and degradation in global confinement.
The transport is gyro-Bohm like and diffusive inside ρ <0.9 and ρ < 0.7 – 0.8 in the normal discharge and thedischarge with the island, respectively. This position
corresponds to the peak position in the density profile.
Outside this position, the transport is non-gyro-Bohm
and/or non-diffusive. At least, the particle transport in thisregion is non-diffusive, since there is a density gradient
without enough particle sources.

IDB discharge (pellet fueled)
1000

(a)
(b)

a2R

.

500

10
5

p

P

H

P

rad

0
40

(c)

(d)

n

e0

20
0
60
40

n
n

Sudo
c

ea

p

e0

20
0

1.5

2

2.5
time (s)3

3.5

Fig.5 Waveforms in a pellet-fueled discharge withheating power reduction after IDB formation,
where (a) the plasma stored energy, Wp, (b)the NB heating power, PH (and the radiation
loss, Prad), (c) the central electron density, ne0(together with the edge density at LCFS, nea,
and the Sudo density limit, ncSudo), and (d) the
central electron pressure, pe0, are shown from
top to bottom.

Internal diffusion barrier (IDB) plasmas are formed
after intense hydrogen ice-pellet injection andcharacterized by high central density, high central pressure,large Shafranov shift, and steep gradient in the core region[13-15]. Relatively low density in the peripheral region
called the mantle [13] is favorable for achieving
high-density, since the density limit in LHD is determinedby the edge electron density at the LCFS, nea [22].
Independent of fueling method, achievable edge density islimited by a semi-empirically determined scaling called theSudo density limit scaling, ncSudo, which is proportional to
the square-root of the heating power [23], i.e.,
PH B

W

0

4. High-Density IDB Plasmas

nea < ncSudo (1020 m-3) = 0.25#87642: R = 3.85 m, B = 2.57 T

discharge shown in Fig. 5. The superdense core region
surrounded by IDB is obviously seen in the profiles of neand pe at t = 2.3 s. Note that the abscissa is given by r/a inFig. 6, for simplicity, since it is difficult to determine theequilibrium of IDB plasmas with high time resolution. The
equilibrium of IDB plasmas with steep pressure gradient in
the core region is still under investigation using HINT2
code [24]. Furthermore, the least-square method has been
carried out to fit the pressure data at 0.5 < r/a < (r/a)max toGB-BFM, to eliminate the data inside IDB.
In spite of the ambiguity in data mapping, the profile
analysis using GB-BFM suggests important features of
IDB plasmas. At first, the pressure profile at t = 3.2 s,
which is well after pellet injection and therefore the IDB islost completely, is well reproduced by the GB-BFM as
seen in the bottom of Fig. 6. The transport property insideof ρ < 0.9 is gyro-Bohm like and diffusive, in this timeslice. Secondly, according to the radial profile ofpe(r/a)/pGB-BFM(r/a) at t = 2.3 s, the mantle pressure is well
reproduced by the GB-BFM, while the core pressure inside
IDB is not. This means that the transport in the mantle
region is gyro-Bohm like and diffusive, while it isimproved inside IDB. Thirdly, the core confinement during
pellet injection (t = 1.9 s) is deteriorated compared with

(6)

When nea exceeds this limit, the hot plasma column begins
to shrink. Then, one should stop further fueling; otherwise
the plasma would collapse radiatively. A high-level ofrecycling can also cause radiative collapse of high-density
plasmas near the density limit. On the other hand, one canincrease the central density as long as the edge density is
kept lower than ncSudo. This has been demonstrated in the
discharge shown in Fig. 5, where PNB was reduced from 11
MW to 3 MW after IDB formation. In spite of a large
reduction in the heating power, the condition of nea < ncSudo
was satisfied and high-density plasma of the order of 1020
m-3 was sustained until the NB was stopped.
In Fig. 6 shown are the radial profiles of Te, ne, pe,pe(r/a)/(ne(r/a)0.6 PH0.4 B0.8), and pe(r/a)/pGB-BFM(r/a), at t =1.9 s (during pellet injection (PI)), 2.3 s (IDB phase justafter PNB reduction), and 3.2 s (without IDB), in the98

J. Miyazawa et al., Bessel Function Model of the Electron Pressure Profile Normalized by Gyro-Bohm Type Parameter Dependence

IDB discharge (pellet fueled)

GB-BFM using the height and width of the pressure profile
as fitting parameters of C and α, respectively. The
equilibrium and fitting region are also optimized tominimize the chi-square.
Using GB-BFM, the followings have been clarified;#87642: R = 3.85 m, B = 2.57 T

(a)

0.5
0

(b)

50

T

t = 2.3 set = 3.2 s
t = 1.9 s (during PI)n1) In normal plasmas fueled by gas-puffing, the transport
inside the density peak around ρ ~ 0.7 – 0.9 isgyro-Bohm like and diffusive.
2) In the edge region of ρ ~ 1 (outside of the density peak),the transport is non-gyro-Bohm and/or non-diffusive.
3) A large magnetic island causes shrinking of theconfinement region and degradation in the global
confinement.
4) The energy transport in the mantle region of IDB
plasmas is gyro-Bohm like and diffusive, as ingas-fueled plasmas.

e

0
40 pe

(c)

20
0
p / (n

(d)

1

e

0.6
e

P

0.4
H

B

0.8
0

)

0
1.5 pe / pGB-BFM

(e)

1
0.5

Fig.6

To improve GB-BFM to reproduce the pressure profile inplasmas with non-parabolic heat deposition, it is necessary
to include the heat deposition profile into the model.

-1

-0.5

0

r/a

0.5

Acknowledgements

1This work is partly supported by NIFS09ULPP517.

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[1]

Radial profiles of (a) the electron temperature,(b) the electron density, (c) the electronpressure, (d) the gyro-Bohm normalized
electron pressure, pe(r/a)/(ne(r/a)0.6PH0.4B0.8), and(e) the ratio of pe(r/a) to pGB-BFM(r/a), in the
discharge shown in Fig. 5. The abscissa is given
by r/a. The least-square method has been carriedout to fit the pressure data at 0.5 < r/a < (r/a)max
to GB-BFM. The mantle region is shaded.

GB-BFM. This might be probably due to the lack ofcentral heating power. At that time, the peripheral density
is as high as ~ 4 × 1020 m-3 at r/a ~ 0.5. The high peripheral
density prevents deep penetration of NB and the heat
deposition moves from the core to periphery [25].
As was noted in Section 2 (below Eq. (3)), theGB-BFM is applicable to the plasmas with parabolic heat
deposition profiles as PH(ρ) ~ J0(2.4ρ). Therefore, lack of(or, excess of) central heating power compared with theparabolic heating profile can cause the deviation ofpressure profile from GB-BFM. To reproduce the pressure
profile with non-parabolic heating profile, it would benecessary to include the heat deposition profile, as thedensity profile, into the model.

5. Summary

A model of electron pressure profile (GB-BFM) has
been constructed based on the diffusion in cylindricalplasmas with gyro-Bohm type parameter dependence.
Then, it has been applied to the profile analysis on plasmas
with a large magnetic island or IDB. In the analysis, themeasured electron pressure profile has been fitted to the99