# Wallace

Document Sample

```					PARS Workshop November 2002

Short-pulse Heating: Theory, Experiments and Scaling

Tom Wallace
tom.wallace@apti.com

Outline

Time domain measurements and impulse responses
• Very simple way to predict results of “conventional” heating vs. f
• Also shows how to optimize scanning
Impulse and frequency responses
• Ionospheric heating
• Earth-ionosphere waveguide
Implications for higher power facilities
• What will the full HAARP facility produce?
• Will the optimum heating frequency change?

Time-Domain Measurements

When we measure an ionospheric signal in the time
domain, we see the convolution of the response of
the ionosphere to heating with the response of the
Earth-ionosphere waveguide
With high time resolution measurements of short
heating pulses, these two responses can be easily
separated and examined
Recent time-domain measurements agree very well
with theory and simulation

Impulse Response of the Ionosphere

Short pulse heating allows us to measure the impulse
response of the ionosphere directly:
• Under the heated region, there are ~500 ms before the
first echo arrives (~150 km round trip)
• The impulse response typically lasts about 200 ms

Which Impulse Response to Look At?

S(t) from a short heating pulse:                                                 B(t) from the same pulse:

)   0.12                                                                     )   2.5
s                                                                            s
t                                                                            t
i                                                                            i
n                                                                            n     2
u    0.1                                                                     u
y                                                                            y
r                                                                            r   1.5
a   0.08                                                                     a
r                                                                            r
t                                                                            t
i                                                                            i     1
b                                                                            b
r   0.06
r
a                                                                            a   0.5
(                                                                            (
S   0.04                                                                     B
A
0

0.02
-0.5

0                                                                            -1
0   0.2   0.4   0.6   0.8       1     1.2   1.4   1.6   1.8   2              0   0.1   0.2   0.3   0.4      0.5    0.6   0.7   0.8   0.9   1
Time (ms)                                                                    Time (ms)

In the past, we’ve looked at S(t) as a measure of performance in simulations.
Looking at B(t) is generally more useful, and it can be experimentally measured.

Why Does B(t) Look Like This?

m0 È                   ˆ
r ∂                       ˆ
r˘
B ( x, t ) =    Ú ÍJ[x, t ' ]ret ¥ r 2 + ∂t J[x, t ' ]ret ¥ cr ˙ dV
4p V Î                                            ˚
If Ú J dV ª ÓEA, r ^ J and large compared to the size
of the source region, and E is constant,

AEm 0          È         r ∂       ˘
B(x, t ) ª      2         Í Ó(t ) + c ∂t Ó(t )˙
4p r           Î                   ˚
So the magnetic field depends on both S(t) and its time derivative;
in fact, the derivative is usually more important even at close range

What Determines S(t) and its Time Derivative?

Maximum value of S: electron density profile (ne vs. h), heated
temperature profile (Te vs. h)
Heated temperature profile: electron density profile, nonlinearly
on quiver energy (e.g. runaway)

Turn-on time constant: quiver energy and temperature profile
Turn-off time constant: temperature profile

Electron density profile is critical to determining heating
altitude; all the following simulations use Barr & Stubbe’s
profile 2 (normal nighttime polar ionosphere) and give good
agreement with measurements.

Impulse Response of 3.3 MHz Ionospheric Heating
Current HAARP FDP 960 kW X-mode
)   2.5
s
t
i
n     2
u

y
r   1.5
a
r
t
i     1
b
r
a   0.5
(

B
0

-0.5

-1
0   0.1   0.2   0.3   0.4      0.5    0.6   0.7   0.8   0.9   1
Time (ms)

Frequency Response of 3.3 MHz Ionospheric Heating
Current HAARP FDP 960 kW X-mode
70

60

50
e
s
n   40
o
p
s
e   30
R

20

10

0
1               2                 3    4
10              10                 10   10
Frequency (Hz)

Impulse Response of the EIW at 0 km Range

Observed values of the reflection coefficient R are 0.2-0.3
1
•
h(t ) = Â R nd (t - t r - (2n + 1) h / c )
0.9

0.8                       n =0

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
0    0.5        1             1.5      2   2.5          3
Time (ms)

Frequency Response at 0 km Range

1.5

e    1
s
n
o
p
s
e
R
0.5

0
1               2                 3    4
10              10                 10   10
Frequency (Hz)

Combined 3.3 MHz Response at 0 km

90

80

70

e   60
s
n
o   50
p
s
e   40
R
30

20

10

0
1               2                  3    4
10              10                  10   10
Frequency (Hz)

Experimental 3.3 MHz Frequency Response at 12 km
k
H
2
z                     3.3 MHz Heating on 4 March 2001
o 1.4
t
d
e
r
a 1.2
p
m
o
C
1
l
e
v
e
L
0.8
d
l
e
i
F
0.6
e
g
a
r
e 0.4
v
A

0.2

0
2                            3                  4
10                           10                 10
Frequency (Hz)

Impulse Response of the EIW at a Distance

Source

h

•
2
h(t ) = Â R nd Ê t - t r - (2n + 1) h 2 + (d / (2n + 1)) / c ˆ
Á                                             ˜
n =0   Ë                                             ¯

Impulse Response of the EIW at 500 km Range

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
0    0.5       1          1.5      2   2.5   3
Time (ms)

Frequency Response of the EIW at 500 km

1.5

e    1
s
n
o
p
s
e
R
0.5

0
1               2                  3    4
10              10                  10   10
Frequency (Hz)

Combined 3.3 MHz Response at 500 km

70

60

50
e
s
n   40
o
p
s
e   30
R

20

10

0
1               2                  3    4
10              10                  10   10
Frequency (Hz)

3.3 MHz Temperature Profile for Full HAARP Facility

Temperature after 500 ms heating
90

85

80

)
m 75
k
(
e 70
d
u
t 65
i
t
l
A 60

55

50

45

40
0   500     1000              1500            2000   2500   3000
Electron Temperature (K)

Full HAARP 3.3 MHz Impulse Response

)   14
s
t
i
n   12
u

y   10
r
a
r   8
t
i
b   6
r
a
(
4
B

2

0

-2
0   0.1   0.2   0.3   0.4      0.5    0.6   0.7   0.8   0.9   1
Time (ms)

Full HAARP 3.3 MHz Frequency Spectrum
Full HAARP 3.6 MW X-mode
350

300

250
e
s
n   200
o
p
s
e   150
R

100

50

0
1               2                 3    4
10              10                 10   10
Frequency (Hz)

Ratio of Full HAARP to Current FDP Field

10

9

8

7

o
i   6
t
a
R   5

4

3

2

1
1                2                 3    4
10               10                 10   10
Frequency (Hz)

Full HAARP 3.3 MHz Heating at 0 km Range
Predicted Response for “Conventional” Heating
500

450

400

350
e
s   300
n
o
p   250
s
e
R   200

150

100

50

0
1               2                  3      4
10              10                  10    10
Frequency (Hz)

Full HAARP 3.3 MHz Heating at 500 km Range
Predicted Response for “Conventional” Heating
400

350

300

e
s   250
n
o
p   200
s
e
R   150

100

50

0
1               2                  3        4
10               10                 10       10
Frequency (Hz)

Summary

“Conventional” heating is predicted to produce
higher fields than the ~3.75x increase expected
from a simple power scaling (result of faster
heating and runaway)
Not yet clear what to expect at higher frequencies
with full HAARP
• Higher frequencies mean higher heating altitudes; this
produces higher S(t), but slower changes
This result will suggest optimum scanning strategy
for the full HAARP