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| **Princeton Plasma |                      |      |                  |
| Physics            |                      |      |                  |
| Laboratory**       |                      |      |                  |
|                    |                      |      |                  |
| **NSTX             |                      |      |                  |
| Experimental       |                      |      |                  |
| Proposal**         |                      |      |                  |
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| **Title:**         |                      |      |                  |
| **Beta-induced     |                      |      |                  |
| Alfven-acoustic    |                      |      |                  |
| modes (BAAE),      |                      |      |                  |
| three wave         |                      |      |                  |
| coupling, and HHFW |                      |      |                  |
| stabilization of   |                      |      |                  |
| CAE/GAE chirping** |                      |      |                  |
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+--------------------+----------------------+------+------------------+
| **PROPOSAL         |                      |      |                  |
| APPROVALS**        |                      |      |                  |
+--------------------+----------------------+------+------------------+
| **Author: N. N.    |                      |      | > Date April 30, |
| Gorelenkov**       |                      |      | > 2007           |
+--------------------+----------------------+------+------------------+
| **ATI -- ET Group  |                      |      | > Date           |
| Leader: S.         |                      |      |                  |
| Sabbagh**          |                      |      |                  |
+--------------------+----------------------+------+------------------+
| **RLM - Run        |                      |      | > Date           |
| Coordinator: D.    |                      |      |                  |
| Gates**            |                      |      |                  |
+--------------------+----------------------+------+------------------+
| **Responsible      |                      |      |                  |
| Division:          |                      |      |                  |
| Experimental       |                      |      |                  |
| Research           |                      |      |                  |
| Operations**       |                      |      |                  |
+--------------------+----------------------+------+------------------+
| [**Chit Review     |                      |      |                  |
| Board**            |                      |      |                  |
| (designated by Run |                      |      |                  |
| Coordin            |                      |      |                  |
| ator)]{.underline} |                      |      |                  |
+--------------------+----------------------+------+------------------+
| **MINOR            |                      |      |                  |
| MODIFICATIONS**    |                      |      |                  |
| (Approved by       |                      |      |                  |
| Experimental       |                      |      |                  |
| Research           |                      |      |                  |
| Operations)        |                      |      |                  |
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|                    |                      |      |                  |
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**NSTX EXPERIMENTAL PROPOSAL**

Beta-induced Alfven-acoustic modes (BAAE), three wave coupling, and HHFW
stabilization of CAE/GAE chirping

*Goals: Characterize and assess 1) the effects of supra-Alfvénic fast
ion driven BAAEs on their confinement and driven current in the plasma
core; 2) three wave coupling of several MHD instabilities; 3)
stabilization of high-f modes, GAE/CAE during HHFW.*

*OP-XP-741*

# **1. Overview of planned experiment** 

The core of the proposed experiment is to investigate predicted,
potentially new, MHD eigenmodes, which are due to coupling of two
fundamental MHD branches Alfvénic and acoustic. Previously identified
L-mode plasma conditions under which Beta-induced Alfvén-acoustic
eigenmodes (BAAE) were observed will be reproduced as initial plasma
condition. Measurements of the eigenmode structure will be performed
with the 5-8 channels of the UCLA reflectometer so that the plasma
density should be relatively low n=3.5x10^13^cm^-3^. At the same time,
the evolution of the current profile will be measured with MSE and
complete equilibrium diagnostic data will be collected. After BAAE modes
will be identified, multiple, identical shots will be made to allow an
NPA scan.

In previous observations plasma rotation was high, f~rot~\~40kHz in the
center and played a negative role in unambiguous mode identification as
the rotation and its shear were ramping during the discharge. We are
planning to apply resonant-error-field braking to avoid or minimize the
rotation effect.

As often in NSTX NBI heated plasmas three wave coupling is expected and
will be explored in order to investigate several effects, such as beam
ion loss and redistribution.

Early applied HHFW is desirable to heat electrons and increase their
beta without heating ions to avoid high ion Landau damping of BAAEs.
These conditions will be compared with later stages of the BAAE
instabilities after electron and background ion betas will be
comparable. At the same time if applied early HHFW will likely effect
the chirping of high frequency modes, such as GAEs/CAEs, which are often
seen at the beginning of the discharge. This is aimed at the goal of a
third part of the proposal, which is to investigate the HHFW introduced
velocity scattering of beam ions on GAE/CAE chirping rate.

# **2. Theoretical/ empirical justification**

Discovery of new global BAAE modes on NSTX, and on JET could be of
importance to ITER with finite plasma beta. These modes may be an
ultimate explanation of some fishbone-like low-frequency instabilities,
often observed with fast frequency chirps. BAAEs are correlated with
fast ion losses, just like TAEs. Three-wave interactions were observed
to correlate with fast ion losses, and have been recently observed
between such low frequency modes and higher frequency Alfvén eigenmodes
(see Figure 1). When three-wave interaction is weak, good agreement
between measurement and theory is expected. When it is strong,
comparison between theory and measurement may reveal the effects of the
interaction.

The proposed experiment would measure eigenmode radial structure to
validate identification of the mode with the ideal code NOVA. An
important tool would be to minimize rotation shear to simplify
interpretation of these modes. Since plasma beta in NSTX is rather high
in comparison with JET beta, it can be considered complimentary to JET
observations. Figure 2 shows the possible target magnetic signal
frequency spectrum and results of its analysis using NOVA code, which
used the q-profile (shown in subfigure c) from 8 channel MSE
measurements. As one can see the modes at n=2 are located at the minimum
of safety factor profile, which turns out to be at the strongest
toroidal shear radial point. Note that obtained BAAE frequency corrected
by the Doppler shift is about 90kHz in the lab frame, which is in good
agreement with the data at t=0.26sec(see figure 2 (left)). However
before that the simulated BAAE frequency is below the frequency of the
observed activity. Removing uncertainty associated with the toroidal
plasma rotation will help to identify the magnetic activity by measuring
its mode structure, polarization and frequency.

Figure 3 shows previous NSTX shot with GAE/CAE chirp (Angel fish)
observations and the effect of the HHFW on the repetition and frequency
chirping rates. The blow-up figure 3b demonstrates the extent of
chirping and how much it is reduced. However, just before the end of the
heating there is the onset of another symmetric chirp signal, perhaps an
indication that extra rf power allows a change of equilibrium parameters
that lead to an altered character to the chirping pulses.

![](media/image1.png){width="2.61875in"
height="3.55625in"}![](media/image2.png){width="2.6493055555555554in"
height="2.3361111111111112in"}

*Figure 1: (Right) Spectrum vs. time of: a) 50 GHz reflectometer phase
and b) edge magnetic fluctuations. c) Spectra for t = 357.0 -- 357.5 ms
with mode numbers as determined from edge magnetics. Fishbone-like modes
(labled as EPMs) and Alfvén eigenmodes (labeld as TAEs) are indicated.
(Left) Bicoherence of 50 GHz reflectometer for t = 350 -- 375 ms.
Maximum uncertainty is \~ 0.1.*

![](media/image3.png){width="2.00625in"
height="1.6722222222222223in"}![](media/image4.png){width="3.1326388888888888in"
height="1.8284722222222223in"}

![](media/image5.png){width="2.6847222222222222in"
height="1.9333333333333333in"}

*Figure 3: (a)* *Repetition* *of frequency sweeping pulses. (b) Spectral
frequency content of a single pulse vs. time (c)Resonance regions of
energetic particle distribution function, with sweeping signal*

The chirping suppression was not always achieved and we would like to
understand this by changing the applied HHFW power to up to 3MW. This
will ultimately help to study the effect of electron heating (during
HHFW) on BAAE frequency. We expect that the BAAE instability will change
its character as well due to reduced damping from thermal ions at
comparable total plasma pressure.

# **3. Experimental run plan**

The experiment will target plasma conditions similar to shot 115731.
Similar shots from more recent XP-734 (Yuh) exist and should be used as
a target shot, such as 123599. We will start with 1 MA L-mode discharge
(123599 like) where the peak density reached ≈ 3.5 x 10^13^/cm^3^ by 350
ms, but with lower field B=4.5kG. The main study will be focused on BAAE
mode structure measurements with and without non-resonant rotation
breaking. We will have three densities of the plasma with 3.2 x
10^13^/cm^3^, 3.5 x 10^13^/cm^3^, and 3.8 x 10^13^/cm^3^ to shift the
reflectometer channels.

If time would allow we will lower the plasma current to create optimal
conditions for the three wave coupling. Some small scan in the density
evolution may be necessary to optimize the reflectometer diagnostic
measurements. Shot 115731 had only source A with injection starting at
170 ms, but for three wave coupling sources B and C are desirable.

The logic of the XP is the following:

1.  Start XP with only source A conditioned to 90 keV and at B=4.5kG,
    n~e~=3.5x10^13^cm^3^.

    a.  *[If BAAEs are not seen]{.underline}* (below RSAE/TAEs) take
        following actions:

        i.  increase field to B=5.5kG,

        ii. apply source C at t=0.2sec with increased outer plasma/wall
            gap up to 6-10cm,

        iii. if no BAAEs are present, go to 115731 shot conditions.

    b.  *[If BAAEs are seen]{.underline}* proceed to non-resonant
        breaking.

2.  At established conditions (1 above) apply n=3 nonresonant rotation
    breaking with coil current at I~RWM~=1kA from t=0.25 (earlier BAAE
    activity time) with the PCS setup of the shot 123184.

    a.  *[If RWM develops]{.underline}* apply lower current in steps
        from 1 to 0.7 to 0.5 kA and proceed to step 3.

    b.  *[If BAAE activity persist]{.underline}* lower coil current to
        I~RWM~=0.7kA at later time t=0.5sec.

3.  Adjust density to optimize reflectometer data at time of BAAE modes
    with n~e~=3.1x10^13^cm^3^ and n~e~=3.8x10^13^cm^3^. Repeat 2 shots
    without and 2 shots with resonance breaking for each of those two
    densities.

4.  NPA will be applied at different tangential radii for each plasma
    density for horizontal scan: R~tan~=100cm for n~e~=3.1x10^13^cm^3^,
    R~tan~=75cm for n~e~=3.5x10^13^cm^3^, and R~tan~=50cm for
    n~e~=3.8x10^13^cm^3^.

5.  At the end of this part of the XP apply small Argon doping for SXR
    rays BAAE diagnostic -- 2 shots in n~e~=3.5x10^13^cm^3^ plasma.

6.  The following is for the possible extension of the XP, that is if
    more time will be allocated.

    a.  To accommodate three-wave coupling we will start with source A
        again and switch to B and C (1 MW each) at t=250msec. Again two
        shots with and two shots without rotation breaking. Switch back
        to source A at the end of the shot for MSE measurements.

        i.  If three-wave coupling is not observed we move toward
            conditions of the shot 120124 with lower plasma current
            Ip=800kA and earlier start of B and C sources.

    b.  To accommodate the study of HHFW effect on angel fish behavior
        we will apply RF at those times when angel fish is seen,
        typically at the beginning of the discharge. RF effects on BAAE
        is of interest as well. Thus we will need to apply it at times
        when BAAEs are seen.

# **4. Required machine, NBI, RF, CHI and diagnostic capabilities**

Describe any prerequisite conditions, development, XPs or XMPs needed.\
Attach completed Physics Operations Request and Diagnostic Checklist

> Toroidal field of 4.5 kG. MSE, multi-channel reflectometer, NPA are
> required. High-k and FIReTIP diagnostics are needed to complement the
> reflectometer data.

# **5. Planned analysis**

What analysis of the data will be required: EFIT, TRANSP, etc.

Extensive TRANSP analysis to calculate fast ion distribution. As much
useful data as possible will be used to benchmark M3D-k and NOVA
simulations. NOVA-KN, nonperturbative code analysis maybe be required to
identify the fishbone and BAAEs as two possible candidates in
explanations of such rather low frequency activity in presence of strong
damping and drives from background plasma and fast ions.

# **6. Planned publication of results**

What will be the final disposition of the results; where will results be
published and when?

> Results of BAAE observations would be reported in the invited talk at
> the EPS meeting 2007 and in the subsequent publication after the
> meeting.

PHYSICS OPERATIONS REQUEST

Beta-induced Alfven-acoustic modes (BAAE), three wave coupling, and HHFW
stabilization of CAE/GAE chirping OP-XP-741

Machine conditions (specify ranges as appropriate)

> I~TF~ (kA): **34-52** Flattop start/stop (s): **0.0/1.0**

I~P~ (MA): **0.8-1.0** Flattop start/stop (s): **0.2/0.9**

Configuration: **123599**

> Outer gap (m): **\_\_\_\_\_**, Inner gap (m): **\_\_\_\_\_**
>
> Elongation : **\_\_\_\_\_**, Triangularity : **\_\_\_\_\_**
>
> Z position (m): **0.00**
>
> Gas Species: **D** , Injector: **Midplane / Inner wall / Lower Dome**
>
> NBI - Species: **D**, Sources: **A/B/C**, Voltage (kV): **90/-/90**,
> Duration (s): **0.90**

ICRF -- Power (MW): **-/2** Phasing: **Heating / CD**, Duration (s):
**0.2**

CHI: **Off**

*Either:* List previous shot numbers for setup: **123599**

*Or:* Sketch the desired time profiles, including inner and outer gaps,
, , heating, fuelling, etc. as appropriate. Accurately label the sketch
with times and values.

**DIAGNOSTIC CHECKLIST**

**Beta-induced Alfven-acoustic modes (BAAE), three wave coupling, and
HHFW stabilization of CAE/GAE chirping OP-XP-741**