Excitation of waves by a spiraling ion beam in a

large magnetized plasma

Shreekrishna Tripathi1, Bart Van Compernolle1, Walter Gekelman1, Patrick Pribyl1, William Heidbrink2

1Department of Physics and Astronomy, UCLA2Department of Physics and Astronomy, UCI

Work jointly supported by US DOE and NSF and performed at the Basic Plasma Science Facility, UCLA

14th IAEA TM on Energetic Particles in Magnetic Confinement Systems , September 1-4, 2015, Vienna, Austria

Main results An intense spiraling ion beam (25 kV/10 A, 0.5–1.5 ms pulse-width) has

been injected into a large magnetoplasma and spontaneous excitationof waves in the shear Alfvén, ion cyclotron, and lower hybrid frequencyranges has been investigated.

Generation of shear Alfvén waves through Doppler-shifted ioncyclotron resonance (DICR) with the ion beam has been confirmed.

The DICR process is particularly effective in exciting left-handedpolarized Alfvén waves that propagate in the direction opposite to theion beam.

At higher frequencies (𝒇𝒇𝒄𝒄𝒄𝒄 ≪ 𝒇𝒇 ≤ 𝒇𝒇𝒍𝒍𝒍𝒍 ), electrostatic waves withspectra showing up to 100 harmonics of the beam gyro-frequency areobserved. The dispersion is consistent with the Doppler shifted beammodes 𝝎𝝎−𝒎𝒎𝛀𝛀𝒄𝒄 = 𝒌𝒌∥𝒗𝒗𝒃𝒃∥ .

2

The Large Plasma Device (LAPD)

Plasma length : 19 mDiameter: 60 cmMagnetic Field : 400 - 2500 GaussRep rate: 1 HzPlasma duration: 5 - 20 ms

Density: 1010 - 4.0x1012 cm-3

Te: 0.5 - 12.0 eVTi: 0.5 - 1.0 eVDischarge Current: 11 kA (max)Discharge Voltage: 40-70 V 3

4

Prior results on energetic particle studies on the LAPD Periodic variation in the ambient magnetic field modulates the Alfvén wave

spectra and creates propagation gap at the Bragg frequency like TAE gap in Tokamaks (Zhang, Phys. Plasmas 15 (2008) 012103).

Use test particle sources to study the fast-ion transport by antenna launched shear Alfven waves (Zhang, Phys. Plasmas 16 (2009) 055706).

Fast-ion transport due to drift-wave turbulence using a lithium test-particle ion beam. Lower energy fast-ions were observed to undergo more transport (Zhou, Phys. Plasmas 19 (2012) 055904).

Scattering of magnetic mirror trapped energetic electrons by Alfvén waves (Wang, Phys. Rev. Lett. 108 (2012) 105002).

Electron beam driven Whistler waves exhibiting fast frequency chirping. This experiment has relevance to Whistler mode chorus waves in the magnetosphere (Van Compernolle, Phys. Rev. Lett. 114 (2015) 245002).

More references at http://plasma.physics.ucla.edu/

1. Fast-ion experiments on the LAPD require an ion beam injection

2. Charge exchange is the dominant loss mechanism of fast-ions on the LAPD

3. The ion beam is nearly collisionless

Barnett & Reynolds, Phys. Rev., Vol. 109, (1958), 355Tripathi, Pribyl, & Gekelman, Rev. Sci. Instrum. 82, 093501 (2011) 5

Charge exchange, ionization , and Coulomb collision mean free paths for the ion beamλcex≈ 10-23 m λionz≈ 92-231 mλibe≈ 399 m (main plasma)λibe≈ 3057 m (afterglow)

λibe >> plasma length

6Intense ion source on LAPD

LAPD END(OPPOSITE PLASMA SOURCE)

PIVOT Beam extractorFocusing Coils

Ion Source Vacuum Chamber

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Cathode

Axial location of the beam injection

Axial location of end magnets

Bz (kG)

10 Br (kG)

Ambient magnetic field profile on the LAPD

Ion beam injected from the low ambient field region outside LAPD magnets.Therefore, the beam divergence in the ion source should be minimized

Beam pitch angle increases in the LAPD plasma due to ⁄𝒗𝒗⊥𝟐𝟐 𝑩𝑩𝟎𝟎 conservation.

Ebeam: 18 keV, Injection Angle: 4°, Beam divergence = 0°, 400 Particles

Computed ion-beam trajectory

Cathode

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9Density and electron temperature profiles of the plasma

A 15 keV/10A H+ beam was injected into a dual-species magnetized plasma. nHe= 0.92ne , nH= 0.08ne

The beam was sub-Alfvénic and waves were in the inertial regime.vbǁ/vA = 0.20, vthe/vA = 0.18

The ambient plasma profile was significantly modified by the beam.

Distance from the exit grid: 4.9 mBeam density: 5.2x109 cm-3

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Distance from the exit grid: 17.7 mBeam density: 2.1x109 cm-3

H+, 15 keV, 10 A, Pitch angle = 53°, B: 1800 G, Rib: 7.8 cm

Measured current-density profiles of the ion-beam

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200100

0-100-200

3015

0-15-30

Typical time traces of beam driven fluctuations

Cherenkov radiation burst at the beam-front

Saturation phase

Spectrum showing Alfven wave propagation in two distinct bands

|B(m

G)|

f (MHz)

Fci (He) Fci (H)

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Cross-field structure of beam destabilized low frequency modes

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Doppler-shifted ion cyclotron and Landau resonances

The Doppler-shifted ion cyclotron resonance (DICR) condition is governed by, 𝝎𝝎 = 𝒏𝒏𝝎𝝎𝒄𝒄𝒃𝒃 + 𝒌𝒌∥𝒗𝒗𝒃𝒃∥

The DICR and Landau resonance conditions can be expressed in terms of cyclotron resonance function C and Landau resonance function L

𝑪𝑪 = 𝒇𝒇𝒇𝒇𝒄𝒄𝒃𝒃

𝟏𝟏 − 𝑺𝑺𝒗𝒗𝒃𝒃∥𝒗𝒗𝝓𝝓∥

𝑳𝑳 = 𝒗𝒗𝒃𝒃∥𝒗𝒗𝝓𝝓∥

𝑺𝑺 = +𝟏𝟏 for co-propagating waves𝑺𝑺 = −𝟏𝟏 for counter-propagating waves

DICR condition may be satisfied when 𝑪𝑪 = ±𝟏𝟏, ±𝟐𝟐, ±𝟑𝟑,⋯ Landau resonance condition may be satisfied when 𝑳𝑳 = 𝟏𝟏 For normal DICR (positive C) with an ion beam, Alfvén waves must counter-

propagate with the ion beam (S = -1).

For anomalous DICR (negative C) with an ion beam, Alfvén waves must propagate in the direction of a super-Alfvénic ion beam (S = 1).

Tripathi et al., Phys. Rev. E 91, 013109 (2015)

LF UF

fci(He) fii

f/fci(He)14

Dispersion relation of shear Alfvén waves in a uniform magnetized plasma𝑘𝑘∥ = 𝑘𝑘0 𝜖𝜖⊥ 1 − 𝑘𝑘⊥2/ 𝑘𝑘02𝜖𝜖∥ 1/2, when 𝜆𝜆⊥ < 𝑐𝑐

𝜔𝜔𝑝𝑝𝑝𝑝(ion inertial length)

For a multi-species cold plasma

𝜖𝜖⊥ = 1 −�𝑗𝑗

𝑓𝑓𝑝𝑝𝑗𝑗2

𝑓𝑓2 − 𝑓𝑓𝑐𝑐𝑗𝑗2, 𝜖𝜖∥ = 1 −�

𝑗𝑗

𝑓𝑓𝑝𝑝𝑗𝑗2

𝑓𝑓2 , 𝑓𝑓𝑖𝑖𝑖𝑖 =(𝑓𝑓𝑝𝑝12 𝑓𝑓𝑐𝑐22 + 𝑓𝑓𝑝𝑝22 𝑓𝑓𝑐𝑐12 )

(𝑓𝑓𝑝𝑝12 + 𝑓𝑓𝑝𝑝22 )

fci(H)

Vincena et al., Phys. Plasmas 20, 012111 (2013)

15Experimental confirmation of the DICR excitation of Alfvén waves

C ,L

f/fci(He)

16Cross-field structure of the Alfvén wave at the DICR frequency

• f/fci,He = 3.67, f=2516 kHz, ∆ f=24 kHz• Left-handed polarization in the middle, mixed polarization in the edge• Structure rotates in the left-handed direction ⇒ shear Alfvén waves• Phase measurements suggest counter-propagation of the wave ⇒ S = -1• Measured ⁄𝒗𝒗𝝓𝝓∥ 𝒗𝒗𝑨𝑨 = 𝟐𝟐.𝟗𝟗𝟗𝟗• Estimated ⁄𝒗𝒗𝝓𝝓∥ 𝒗𝒗𝑨𝑨 = 𝟐𝟐.𝟖𝟖𝟖𝟖 (from dispersion relation of shear Alfvén wave)

17High-frequency beam modes (f >> fci)

Broad spectra with distinct peaks close to harmonics of the beam gyro-frequency. The peaks in the spectra extend out to the 100th harmonics in some cases.

Beam gyro-frequency harmonics

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Cross-field structure of the Ey wave-field component ( wave localized near the beam orbit ⇒ not a global mode )

Approximate beam orbit

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The high frequency waves contain larger 𝒌𝒌⊥at higher harmonics

𝒌𝒌⊥ spectrum 𝒌𝒌⊥ spectrum

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Cross-field dispersion of the high-frequency waves

The fitted line corresponds to 𝒗𝒗𝒃𝒃⊥ of 15 keV He+ beam with 33° pitch-angle. The dispersion relation is of the form 𝝎𝝎 ≃ 𝒌𝒌⊥𝒗𝒗𝒃𝒃⊥, which corresponds to 𝝎𝝎 ≃ 𝒎𝒎𝛀𝛀𝒄𝒄 (𝒌𝒌⊥ = ⁄𝒎𝒎 𝑹𝑹 and 𝒗𝒗𝒃𝒃⊥ = 𝑹𝑹𝛀𝛀𝒄𝒄)

21Near perpendicular propagation of high frequency waves

Peaks in the spectra are shifted away from harmonics by 50—200 kHz. The exact dispersion relation predicts shift, 𝝎𝝎−𝒎𝒎𝛀𝛀𝒄𝒄 = 𝒌𝒌∥𝒗𝒗𝒃𝒃∥ This implies 𝒌𝒌∥ ≈ 0.005 cm-1 and ⁄𝒌𝒌⊥ 𝒌𝒌∥ ∼ 103 and indicates near

perpendicular propagation of these high frequency waves.

Main results An intense spiraling ion beam (25 kV/10 A, 0.5–1.5 ms pulse-width) has

been injected into a large magnetoplasma and spontaneous excitationof waves in the shear Alfvén, ion cyclotron, and lower hybrid frequencyranges has been investigated.

Generation of shear Alfvén waves through Doppler-shifted ioncyclotron resonance (DICR) with the ion beam has been confirmed.

The DICR process is particularly effective in exciting left-handedpolarized Alfvén waves that propagate in the direction opposite to theion beam.

At higher frequencies (𝒇𝒇𝒄𝒄𝒄𝒄 ≪ 𝒇𝒇 ≤ 𝒇𝒇𝒍𝒍𝒍𝒍 ), electrostatic waves withspectra showing up to 100 harmonics of the beam gyro-frequency areobserved. The dispersion is consistent with the Doppler shifted beammodes 𝝎𝝎−𝒎𝒎𝛀𝛀𝒄𝒄 = 𝒌𝒌∥𝒗𝒗𝒃𝒃∥ .

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Future research Explore the anomalous DICR in destabilizing the Alfvén waves using a

LaB6 plasma source (higher ne ⇒ lower vA ⇒ vb/vA ≈ 2.0) on the LAPD.

Cherenkov radiation of Alfvén waves.

Plasma production by the ion beam on the LAPD.

Collaborative efforts to model the beam-plasma experiments.23

Image of the He plasma produced by the LaB6 source

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Cross-field structure of the Alfvén wave in the LF band ( ⁄𝒇𝒇 𝒇𝒇𝒄𝒄𝒄𝒄,𝑯𝑯𝑯𝑯 = 𝟎𝟎.𝟗𝟗)

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Ion-beam parameters:

H+, 15 keV, 10 A, Injection angle: 7.5°, Pitch angle = 53°βbeam/ βplasma ≈ 4 - 40Vb: 1.69 x 106 m/s, Vbǁ: 1.02 x 106 m/s, Vbǁ/Vb⊥: 0.75 Beam-spot diameter ≈ 8 cmB: 1800 G, Gyro-radius of the beam: 7.8 cm, fcib = 2.74 MHz Spiral length: 46 m, ∆Z between neighboring orbits= 37.2 cm, Norbit=51

Plasma Parameters:

ne = 1.5x1011cm-3, Te = 5.0 eV, B = 1.8 kG, nHe= 0.92ne , nH= 0.08ne fci1 = 685 kHz, fii = 2385 kHzvA = 5.2 x 106 m/s, vthe/vA = 0.18, vbǁ/vA = 0.20

Charge exchange, Coulomb collisions, and ionization by the H+

beam Cross-section data for 15 keV H+ ions σcex ≈ 4 x 10-16 cm2 (H+ → H)σcex ≈ 2 x 10-16 cm2 (H+ → He)σionz ≈ 1 x 10-16 cm2 (H+ → H)σionz ≈ 1.5 x 10-17 cm2 (H+ → He)

Charge exchange & ionization by the beam in the ion source:Pmax ≈ 5x10-4 Torr (H) (nn = 1.8x1013 cm-3)λcex≈ 1.4 m (min), λionz≈ 5.6 m

Charge exchange & ionization by the beam in the LAPD plasma:P ≈ 3x10-5 Torr (H) ⇒λcex≈ 23 m, λionz≈ 92 mP ≈ 8x10-5 Torr (He) ⇒λcex≈ 18 m, λionz≈ 231 m

Coulomb collisions in the LAPD plasma:n ≈ 2.3x1012 cm-3 , Te ≈ 10 eV, Ti ≈ 0.5 eV ⇒λibe≈ 399 m, λibi≈ 3x106m (main plasma)n ≈ 3.0x1011 cm-3 , Te ≈ 22 eV, Ti ≈ 0.5 eV ⇒λibe≈ 3057 m, λibi≈ 2x107m (50 ms afterglow)

Barnett & Reynolds, Phys. Rev., Vol. 109, (1958), 35526

27Electron heating and plasma production by the beam

Power needed to sustain the plasma• Discharge power from the BaO source to maintain the 1012 cm-3, 5 eV plasma ≈ 150 kW• Discharge power flux in the 25 cm radius plasma ≈ 750 kW/m2

• Power needed to sustain the 12 cm radius beam produced plasma ≈ 34 kWPower balance in the beam• Total power in the injected beam ≈ 150 kW• Power lost by the charge exchange ≈ 75 kW (≈ 50%)• Power lost by the beam scattering ≈ 15 kW (≈ 10%)• Power dissipated in the plasma ≈ 60 kW (≈ 40%) ⇒ sufficient to sustain the plasma

Amplitude increases at higher magnetic field.

At higher harmonics, the waves become more electromagnetic in character.

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Hydrogen Beam in Helium-Hydrogen plasma