![Page 1: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/1.jpg)
MHD in weakly-ionised media
Mark WardleMacquarie University
Sydney, Australia
€
![Page 2: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/2.jpg)
Outline•Molecular clouds and star formation
•MHD in weakly ionised media
•A comment on the hall effect
•Conductivity in molecular clouds
•Shock waves
•Conductivity in protostellar discs
•Implications for MRI and jets
![Page 3: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/3.jpg)
Introduction
![Page 4: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/4.jpg)
![Page 5: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/5.jpg)
![Page 6: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/6.jpg)
![Page 7: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/7.jpg)
![Page 8: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/8.jpg)
![Page 9: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/9.jpg)
![Page 10: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/10.jpg)
![Page 11: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/11.jpg)
Magnetic fields in molecular clouds •Magnetic fields play an important role during star formation
–Pmag is 30–100 times Pgas in molecular clouds–energy density of magnetic field, fluid motions and self-gravity are similar –field removes angular momentum from cloud cores–field diffusion is required to avoid magnetic flux problem
![Page 12: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/12.jpg)
![Page 13: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/13.jpg)
MHD with finite conductivity
![Page 14: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/14.jpg)
![Page 15: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/15.jpg)
Conductivity
![Page 16: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/16.jpg)
The Hall parameter
•relative strength of magnetic and drag forces in determining drift velocity
particles tied to field
particles tied to neutral fluid
![Page 17: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/17.jpg)
•For ions,
•For electrons,
![Page 18: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/18.jpg)
The conductivity tensor•solving for :
•current density:
– field-parallel conductivity
– Hall conductivity
– Pedersen conductivity
![Page 19: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/19.jpg)
Magnetic diffusion
![Page 20: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/20.jpg)
•If the only charged species are ions and electrons,
•Three distinct diffusion regimes:
– Ohmic (resistive)
– Hall
– Ambipolar
log n
log B
ohmic
hall
ambipolar
![Page 21: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/21.jpg)
Hall effect in fully vs weakly ionised plasma•Hall effect arises through asymmetry in tying of charged particles to
magnetic field lines
•Fully ionised plasma: high frequencies, short wavelengths–difference between ion and electron cyclotron frequencies–ions can no longer keep up with changes to field–short lengthscales often irrelevant at the scales of interest–hall MHD etc
•Partially ionised plasma: low frequencies, long wavelengths–difference between ion and electron collision frequencies–neutral collisions decouple ions before electrons–length/time scale may be comparable to system size/evolutionary time scale–conductivity tensor in generalised Ohm’s law
•How does one reconcile these approaches?–in partially ionised case, ions become attached to the neutrals–effective ion mass is increased by ratio of neutral to ion densities–effective cyclotron frequency is reduced by same factor
•Be careful when estimating relevance of Hall effect!!!
![Page 22: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/22.jpg)
4 6 8 10 12 14-6
-4
-2
0
2log B (G)
log n_H (cm^-3)
electronsions
50 A2500 A
solarnebula
molecularclouds
![Page 23: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/23.jpg)
Umebayashi & Nakano 1990
![Page 24: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/24.jpg)
Nishi, Nakano & Umebayashi 1991
![Page 25: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/25.jpg)
Nishi, Nakano & Umebayashi 1991
![Page 26: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/26.jpg)
3 4 5 6 7 8 9 10 11 12 13 14 15-5
-4
-3
-2
-1
0
1
2
3
Ambipolar
Hall
Ohmic
0.1mlo
g
(1015
cm
km
s-1)
log nH (cm-3)
![Page 27: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/27.jpg)
3 4 5 6 7 8 9 10 11 12 13 14 15-5
-4
-3
-2
-1
0
1
2
3
Ambipolar
Hall
Ohmic
MRNlo
g
(1015
cm
km
s-1)
log nH (cm-3)
![Page 28: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/28.jpg)
3 4 5 6 7 8 9 10 11 12 13 14 15-5
-4
-3
-2
-1
0
1
2
3
Ambipolar
Hall
Ohmiclog
(1015
cm
km
s-1)
log nH (cm-3)
MRNi
![Page 29: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/29.jpg)
3 4 5 6 7 8 9 10 11 12 13 14 15-5
-4
-3
-2
-1
0
1
2
3Ambipolar
Hall
Ohmiclog
(1015
cm
km
s-1)
log nH (cm-3)
MRNx
![Page 30: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/30.jpg)
J-type shock waves
![Page 31: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/31.jpg)
![Page 32: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/32.jpg)
C-type shock waves
![Page 33: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/33.jpg)
![Page 34: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/34.jpg)
![Page 35: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/35.jpg)
Instability
![Page 36: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/36.jpg)
![Page 37: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/37.jpg)
Shock waves - Hall effect
![Page 38: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/38.jpg)
Wardle 1998
![Page 39: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/39.jpg)
Wardle 1998
![Page 40: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/40.jpg)
Chapman & Wardle MNRAS in press
![Page 41: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/41.jpg)
Chapman & Wardle MNRAS in press
![Page 42: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/42.jpg)
Stars, protostellar disks and planets
![Page 43: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/43.jpg)
![Page 44: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/44.jpg)
![Page 45: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/45.jpg)
![Page 46: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/46.jpg)
The minimum-mass solar nebula•Simple model for surface density based on the solar system
(Hayashi 1981)–add H,He etc to each planet to recover standard interstellar abundances–spread matter smoothly
•Resulting surface density:
•Disk mass:
•Useful reference standard
![Page 47: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/47.jpg)
•Temperature is estimated by considering thermal balance for a black solid particle
–assume spherical, radius a, distance r from the sun:
•Then:
– disk is thick beyond 30 AU
– self-gravity negligible
![Page 48: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/48.jpg)
![Page 49: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/49.jpg)
![Page 50: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/50.jpg)
![Page 51: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/51.jpg)
![Page 52: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/52.jpg)
![Page 53: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/53.jpg)
![Page 54: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/54.jpg)
![Page 55: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/55.jpg)
![Page 56: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/56.jpg)
![Page 57: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/57.jpg)
![Page 58: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/58.jpg)
Protostellar disks
![Page 59: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/59.jpg)
Bachiller 1996 ARA&A
![Page 60: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/60.jpg)
Bachiller 1996 ARA&A
![Page 61: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/61.jpg)
Kitamura et al 2002 ApJ
![Page 62: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/62.jpg)
Kitamura et al 2002 ApJ
![Page 63: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/63.jpg)
Kitamura et al 2002 ApJ
![Page 64: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/64.jpg)
Kitamura et al 2002 ApJ
![Page 65: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/65.jpg)
Kitamura et al 2002 ApJ
![Page 66: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/66.jpg)
Kitamura et al 2002 ApJ
![Page 67: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/67.jpg)
Protostellar disks•Role of magnetic field in final stages of formation and subsequent
evolution of protoplanetary discs is unclear–MHD turbulence (magnetorotational instability)?–disc-driven MHD winds?–disc corona?–dynamo activity?
•How strong is the magnetic field?
•Is the field coupled to the material in the disc?–disc is weakly ionised
![Page 68: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/68.jpg)
Protostellar disks are poorly conducting•high density implies low conductivity
–recombinations relatively rapid–drag on charged particles
•deeper layers shielded from ionising radiation for r < 5 AU–x-ray attenuation column ~10 g/cm2 –cosmic ray attenuation column ~100 g/cm2
![Page 69: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/69.jpg)
Igea & Glassgold 1999
cosmic rays
x-ray ionisation rate
![Page 70: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/70.jpg)
How strong is the magnetic field?
•Expect B > 10 mG given the strength in cloud cores
•Compression during formation of disk and star
•Shear in disc may wind up field or drive MRI
•Equipartition field in the minimum solar nebula
•Evidence for 0.1 – 1 G fields in the solar nebula at 1AU
![Page 71: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/71.jpg)
Sano & Stone 2002a
![Page 72: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/72.jpg)
Magnetic field diffusion in protostellar disks•Is the magnetic field coupled to the matter?
< h cs ?
•Which diffusion components dominate?–ohmic, hall or ambipolar?
•What are the consequences of different diffusion regimes?–vector evolution of B shows fundamental differences–hall diffusion reverses sign under global field reversal (yikes)
•Diffusion and magnetocentrifugal jet launching–loading of mass onto field lines–constrains bending of field lines within disk–radial drift of field
•Diffusivity depends on location–vertical stratification of ionisation rate and density–inconvenient radial variations of microphysics
![Page 73: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/73.jpg)
Resistivity calculations
•minimum solar nebula–assume isothermal in z-direction
•ionisation by cosmic rays and x-rays from central star
•simple reaction scheme following Nishi, Nakano & Umebayashi (1993)–H+,H3
+,He+,C+,molecular (M+) and metal ions (M+), e-, and charged grains–extended to allow high grain charge (T larger than in molecular clouds)
•adopt model for grains–none, single size grains, MRN size distribution, MRN+ice mantles,
extended MRN, etc–results for “no grains” or 0.1 m grains presented here
•evaluate resistivity components–when can the field couple to the shear in the disc?–which form of diffusion is dominant?
![Page 74: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/74.jpg)
Ionisation products
![Page 75: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/75.jpg)
Reaction scheme
![Page 76: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/76.jpg)
log
n / n
H (s-1)
M+
C+m+
e
He+
H+H3
+
Abundances: 1AU, no grains
z / h
![Page 77: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/77.jpg)
Criterion for coupling
![Page 78: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/78.jpg)
![Page 79: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/79.jpg)
z / h
log
n / n
H
-14
0
1
2
3-13
(s-1)
-11
-12
M+
-4
-3
-2
C+
m+
e
He+
H+H3
+
Abundances: 1AU, 0.1m grains
![Page 80: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/80.jpg)
![Page 81: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/81.jpg)
![Page 82: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/82.jpg)
![Page 83: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/83.jpg)
5 AU
![Page 84: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/84.jpg)
5 AU
![Page 85: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/85.jpg)
5 AU
![Page 86: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/86.jpg)
5 AU
![Page 87: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/87.jpg)
5 AU
![Page 88: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/88.jpg)
5 AU
![Page 89: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/89.jpg)
Magnetorotational instability (MRI)•magnetic field couples different radii in disc
•tension transfers angular momentum outwards
•kh > 1 required to fit in disc, i.e. vA/cs < 1
•resulting turbulence transports angular momentum outwards
![Page 90: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/90.jpg)
MRI in non-ideal MHD
Ambipolar or ohmic diffusion
Hall diffusion
Wardle 1999
![Page 91: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/91.jpg)
Salmeron & Wardle 2005
![Page 92: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/92.jpg)
Salmeron & Wardle 2005
![Page 93: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/93.jpg)
Salmeron PhD thesis
![Page 94: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/94.jpg)
Stone & Fleming 2003
MRI with dead zone
![Page 95: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/95.jpg)
Sano & Stone 2002b
MRI with hall diffusion
![Page 96: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/96.jpg)
Sano & Stone 2002b
logB2/ 8πP0
![Page 97: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/97.jpg)
Protostellar jets
![Page 98: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/98.jpg)
HH 30
![Page 99: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/99.jpg)
Wardle 1997IAU Coll. 163 (astro-ph)
![Page 100: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/100.jpg)
Wardle 1997IAU Coll. 163 (astro-ph)
![Page 101: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/101.jpg)
Salmeron, Wardle & Königl
![Page 102: MHD in weakly-ionised media Mark Wardle Macquarie University Sydney, Australia](https://reader033.vdocuments.net/reader033/viewer/2022051521/5a4d1ade7f8b9ab059975d1b/html5/thumbnails/102.jpg)