Selection and Detection of High-Frequency Relic Gravitational

Waves

Fangyu Li, Zhenya Chen.Chongqing University, Chongqing 400044,.

ChinaRobert M. L. Baker, Jr.

GRAWAVE® LLC, 8123 Tuscany Avenue, Playa del Rey, California 90293, USA

1.1. Motivation and Background.Motivation and Background.

2.2. Outline.Outline.

3.3. Electromagnetic Detection to High-Electromagnetic Detection to High-Frequency Gravitational Waves.Frequency Gravitational Waves.

4.4. Challenges and opportunity.Challenges and opportunity.

Background

Classification of gravitational wave frequency bands.(1) ν~1Hz-104Hz, the detecting region by ground laser interferometer

gravitational wave observatory, such as VIRGO, LIGO, etc.

(2) ν~100Hz-103Hz, the detecting region by the resonant mass detectors, such as Weber Bar.

(3) ν~10-4Hz-1Hz, the detecting region by Laser Interferometer Space Antenna, such as LISA.

(4) ν~10-6Hz-10-3Hz, the detecting region by ASTROD.

(5) ν~107Hz-109Hz, the detecting region by electromagnetic microwave cavity or circular waveguide.

(6) ν~109Hz-1011Hz, the detecting region by coupling system of the microwave beams and static EM fields.

S. W. Hawking: (1979) High-frequency gravitational waves in excess of 100kHz and may have the most promise for terrestrial generation and practical, scientific, and commercial application (Cambridge university press, Cambridge,

98, 1979)

L. D. Landau and E. M. Lifishitz: Since it has definite energy, the gravitational

waves is itself the source of some additional gravitational field… its field is a second-order effect… but in the case of high-frequency gravitational waves the effect is significantly strengthened….

(the Classical Theory of Fields, on page 372, 1975)

Why would we like to study this project?

(1) According to the theory of general relativity, Gravitational waves (GWs) and Electromagnetic (EM) waves have a same propagating velocity in vacuum:

Optimum coherence effect of the two fields may be generated(2) The GHz (~109Hz-1010Hz) are just typical microwave

frequency band, one can use well-considered microwave technology in the frequency region.

( )

( )

g

g e

e

GWs V cV V c

EM waves V c

(3) (under the resonant condition) (3) (under the resonant condition)

Characteristic dimensions of the EM Characteristic dimensions of the EM

detecting system would be L~1-10m, detecting system would be L~1-10m,

they are the typical laboratory they are the typical laboratory

dimensions, and it is easy to construct array.dimensions, and it is easy to construct array.

(4)The microwave beam (e.g., Gaussian (4)The microwave beam (e.g., Gaussian

beam) propagating a static field is an beam) propagating a static field is an

open system in free space.open system in free space.

the EM response has more direct the EM response has more direct

displaying effect.displaying effect.

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Some expected and possible HFGW sources

ν (Hz) h ΩRelic GWs  ~109-1011 ～ 10-30-10-32

(r. m. s)

~10-5-10-6

Solar Plasma  ~1015 ～ 10-39

(on the earth)

Strong EM Systems (e.g. ,see First High-

frequency GW Conference

Proceedings,Mclean,Virginia,USA,2003 )

  ~107-108 ～ 10-29-10-35

(on the focal region)

High Energy Particles

(e.g., Fermi Ring)

 

~104 - 105

～ 10-39-10-40

(on the center)

According to According to Randall-SuRandall-Sundrumndrum models, the HFG models, the HFGWs would be more capaWs would be more capable of carrying energy froble of carrying energy from our m our

3-brane world than lowe3-brane world than lower-frequency GWs by their-frequency GWs by their propagation in the extrr propagation in the extra dimensions,do inverse a dimensions,do inverse effects of the effects of the

R-S models exist for our R-S models exist for our brane world?brane world?

Birmingham University, Birmingham, England

R. Ballantini et.al.,Institute of National Nuclear Physics, Genova, Italy

Unlike the cavity EM response to the HFGWs, a Gaussian beam (GB) passing through a static magnetic field is an open system in the free space, the perturbation photon flux and the background photon flux have very different physical behaviour in the local regions, and the perturbation has more direct observable effect.

Coupling system of fractal membranes and Gaussian beam passing through a static magnetic field

High-frequency relic GWs and their asymptotic behavior in the high-frequency band:

1 3 2 2 3 2( ) [ ( ) ( ) ( ) ( )]. 2

A k J k A k J k

General form of high-frequency constant amplitude GWs is

Asymptotic form in the high-frequency region and in the laboratory frame of reference will be

.(1), (2)Eqs ( , ) ( ) ( ) exp[ ( )]

( ) ( ) exp[ ( )]

g g g

g g g

h x t A k a t i k x t

B k a t i k x t

(3)

(1)

(2)

exp ( )

exp ( )

g g

g g

h A i k x t

h A i k x t

(4)

( )[exp( ) exp( )] , ij ijh ik x ik x e

a

The Gaussian beam with the double transverse polarized electric modes (DTPEM)

2210

22exp exp tan

21

ee e

k rr zi k z t

W f Rz

f

(5)

2(0) (0)

20

2(0) (0)

20

(0)

0

1 2Re exp ,

2

1 2Re exp ,

2

1Re

2

yxx y x

e e

y xy x y

e e

y xz x y

e e e

i rn f

y x W

i rn f

x y W

i in

z

2(0)

2

2exp .z

rf

z W

(6)

0

(0) (1)

1

0

g g g F Jg

F F F

F F F

(7)

High-frequency relic GW:

the tensor perturbation

Gaussian beam +static magnetic field:

background real photons +virtual photons

Synchro-coherent

resonanceωe=ωg

It is possible to produce the perturpative photon flux

(PPF),and the PPF and BPF have very different physical behaviour in some special local

regions

(0) (1) (2)

T T T Tmn mn mn mn= + +

(0) (1) (2)

T T Tmn mn mn? ?

zo

B0

x

y y

x

GW

GW

EMW

Gaussian beam

PPF

PPF

The PPF and the BPF propagate along opposite directions in the regions of 1st, 3rd,6th,and 8th octants,while they have the same propagating directions in the regions of 2nd, 4th , 5th and 7th octants.

X

12

3 4

O

PPF

PPF

PPF

PPF

BPF

BPF

BPF

BPF

Y

Fig 1, the region of z>0

O

Y

X

X

56

7 8

O

PPF

PPF

PPF

PPF

BPF

BPF

BPF

BPF

Y

Fig 2, the region of z<0

O

Y

X

The perturbative photon fluxesThe perturbative photon fluxes

νν(Hz)(Hz) ΩΩ(peak (peak

values)values)

hh(r.m.s)(r.m.s)

l l (m),the (m),the interacting interacting dimensionsdimensions

of static of static magnetic fieldmagnetic field

The PPFs (sThe PPFs (s-1-1))

10101010 1010-6-6 2.00×102.00×10-31-31

0.30.366

2020

2.02 ×102.02 ×104.04×104.04×1022

1.35×101.35×103 3

10101010 1010-5-5 6.32×106.32×10-31-31

0.30.366

2020

6.37×10 6.37×10 1.27×101.27×1033

4.25×104.25×1033

Directional sensitivity of the system

Propagating directions of the resonant components

of the relic GW PPFs (s-1)

z-zxy

1.27×103

3.16×106.30×10-1

0

The thermal noise and the EM noise

For the possible external EM noise sources,using a Faradaycage or shielding covers made from the fractal membranes,ora good “microwave darkroom” might provide an effective shielding environment.

(1) (1) (0) (1)*

0 0

1 1 1Re ( )

2yx

x y z ye e e

in E B E

y x

yy

(0)0 1

2 1/ 2 20

ˆ ( )1

4 [1 ( / ) ] ( / )y g

e

A B k y z l

z f z f z

y 2 (0)

0 112 2 3/ 2

0 0

ˆ ( )sin tan

2 2 [1 ( / ) ]g yk r A B y z lz

R f W z f

y

2 (0) 22 20 11 1

12 2 2 1/ 20

ˆ ( )1 4cos tan exp 1 ( )sin tan

2 4 [1 ( / ) ] 2g y g g

e

k r A B k z l k xz r x zF y

R f W W R z f R f

y

2 2 (0) 20 11 2 1

2 12 2 4 2 1/ 20

ˆ ( )2 1( )cos tan ( )cos tan

2 4 [1 ( / ) ] 2g g y gk x k A B z l k xz z

F y x F yR f W R W z f R f

y

2 21

2 2( ) sin tan exp

2gk x z x

F yR f W

22

1 2( ) exp( )cos( ) ,

2gk yy

F y dyW R

= -ò ,)2

sin()exp()(2

2

2

2 dyR

yk

W

yyF g

where,

The separation of the PPF(signal) from the background photon flux

The distance to the fractal membrane 3.16cm 12cm 42cm 70cm

The background photon flux 2.44×1024 s-1 2.16×1022 s-1 1.27×103 s-1 1.97×10-6 s-1

The PPF reflected or transmitted by the fractal membrane

1.27×103 s-1 1.24×103 s-1 1.21×103 s-1 1.01×103 s-1

Opportunity

1. This scheme might provide a new window and in new way for detection of the HFRGWs in the GHz band.

2. Typical dimensions of the detecting system would be only 1-10m, and constructing cost may be only one percent of LIGO or less.

3. It contains new ideas, new developed results (including theoretical, experimental and technological results)

Difficulties and challenge

1. How to keep a good vacuum environment to avoid the scattering of the photons and the dielectric dissipation.

2. How to reduce further temperature and maintain a good cryogenic environment to suppress relevant thermal noise.

3. How to make a best combination to reduce

and overcome system noise, what is the concrete

form and influence of quantum noise in the system?

4. How to suppress distortion of the shape and the spot

radius of the Gaussian beam, what is concrete

correction and influence of the higher order modes

in the Gaussian beam?

However, because of fast development of relative technology,such as superconductors, nanotechnology, high-quality factor microwave cavities, ultra-fast science,strong field physics, cryogenic technology,strong microwave beam technology, high-energy laboratory astrophysics,etc.

They offered technically possibilities

This subject might become a reality

Thank you！谢谢！