title: Topics in Energy Release and Particle Acceleration in the Heliosphere

authors: Armstrong, Craig Keith

subjects: astrophysics

abstract: This thesis investigates both the release of energy in solar flares, and the acceleration and transport of particles in various astrophysical situations. While numerical simulations are central to this thesis, these are always motivated by analytical arguments.

A review of flare energy release is given in Chapter 2, with results presented in Chapters 3 and 4. The main goal of the flare work is to investigate the effect of viscosity on energy release rates. Scaling arguments and exact solutions of the magnetohydrodynamic equations are used to interpret the results of two-dimensional numerical simulations of magnetic reconnection. The results support viscous energy dissipation accounting for a significant fraction of flare energy release.

Chapter 5 contains an introduction to astrophysical particle acceleration, using the Fokker-Planck formulation. The theory introduced in this chapter is used to study electron transport in solar flare loops (Section 5.5). A key aspect of the analysis is the expression of the Fokker-Planck equation as a system of stochastic differential equations. A generalisation to the flare loop hard X-ray emission prediction of Conway et al. (1998) is obtained, giving a stronger dependence on density for dispersed initial distributions.

Chapter 6 uses the methods of the previous chapter to study the acceleration of cosmic-rays at the heliospheric termination shock. The applicability of the focused acceleration mechanism of Schlickeiser and Shalchi (2008) is examined using numerical simulations, which are interpreted using analytical arguments based on averaging the stochastic equations. The results show significant limitations in assuming a near-isotropic distribution, a requirement for the focused acceleration mechanism. In addition, momentum diffusion provides a significant effect that cannot be neglected.  The theory is extended to include focused deceleration and pure momentum diffusion.

text: Topics in Energy Release and Particle Acceleration in the Heliosphere This thesis investigates both the release of energy in solar flares, and the acceleration and transport of particles in various astrophysical situations. While numerical simulations are central to this thesis, these are always motivated by analytical arguments.

A review of flare energy release is given in Chapter 2, with results presented in Chapters 3 and 4. The main goal of the flare work is to investigate the effect of viscosity on energy release rates. Scaling arguments and exact solutions of the magnetohydrodynamic equations are used to interpret the results of two-dimensional numerical simulations of magnetic reconnection. The results support viscous energy dissipation accounting for a significant fraction of flare energy release.

Chapter 5 contains an introduction to astrophysical particle acceleration, using the Fokker-Planck formulation. The theory introduced in this chapter is used to study electron transport in solar flare loops (Section 5.5). A key aspect of the analysis is the expression of the Fokker-Planck equation as a system of stochastic differential equations. A generalisation to the flare loop hard X-ray emission prediction of Conway et al. (1998) is obtained, giving a stronger dependence on density for dispersed initial distributions.

Chapter 6 uses the methods of the previous chapter to study the acceleration of cosmic-rays at the heliospheric termination shock. The applicability of the focused acceleration mechanism of Schlickeiser and Shalchi (2008) is examined using numerical simulations, which are interpreted using analytical arguments based on averaging the stochastic equations. The results show significant limitations in assuming a near-isotropic distribution, a requirement for the focused acceleration mechanism. In addition, momentum diffusion provides a significant effect that cannot be neglected.  The theory is extended to include focused deceleration and pure momentum diffusion.

year: 2014

title: Uplift history and geomorphic development of the Southern Alps, New Zealand, assessed by fission track analysis

authors: Tippett, J. Mark

abstract: The uplift history and geomorphic development of the Southern Alps has been studied, using fission track analysis of basement samples in combination with measurement of the present geomorphology of the Southern Alps. 

During the late Cenozoic the Pacific plate has been converging obliquely with the Australia plate in South Island, New Zealand. A result of this convergence has been the growth of a major mountain range - the Southern Alps - at the leading edge of the Pacific plate. The results of fission track analysis of 140 samples from 13 transects across the 300 km-long central sector of the Southern Alps reported here, establish the late Cenozoic vertical kinematics (amount, age, and rate of rock uplift) of the Pacific crust underlying the Southern Alps. The pattern of late Cenozoic rock uplift is asymmetrical with respect to the Alpine Fault, being a maximum (19 km) immediately east of the central part of the Fault, with lesser values at the eastern (3 km), northern (10 km) and southern (8 km) extremities of the Southern Alps. The age of the start of rock uplift varies spatially across the Southern Alps, the earliest indications from fission track analysis being at 8 Ma ago at the southern end of the Southern Alps, decreasing to 5 Ma ago at the northern end and 3 Ma ago along the southeastern margin. This age variation reflects the longer time over which the southern parts of the Southern Alps have been in collision. The rate of propagation of rock uplift southeastwards into the Pacific plate has been 30 mm/a, nearly 4 times the late Cenozoic average rate of convergence normal to the plate boundary. Late Cenozoic mean rock uplift rates range from a maximum of ∼2.8 mm/a at the Alpine Fault to a minimum of ∼1.0 mm/a in the east. Uplift has accelerated over time, but only significantly since 1.3 ± 0.3 Ma ago. 

The fission track data in combination with topographic data have been analysed to quantify the response of the surface of the Pacific plate to the late Cenozoic continent-continent collision. The rates of mean surface uplift, the rates of work done against gravity during the mountain building, and the erosional, isostatic and tectonic components (amounts and rates) of rock uplift, have been derived and mapped over the central 300 km length of the Southern Alps. The data do not support the notion of erosional-mechanical coupling of the two wedges in the two-sided orogen model of Koons [1990], but are consistent with overriding of the Australia plate by the Pacific plate. The late Cenozoic rate of mean surface uplift in the Southern Alps ranges from <0.1 mm/a adjacent to the Alpine Fault to >0.3 mm/a over most of the area east of the Main Divide. The highest rates of mean surface uplift do not coincide spatially with the regions of highest mean elevation. The rate of work done in elevating the mean surface ranges from ∼2.5 mWm⁻² to ∼10 mWm⁻², although most areas have experienced similar rates of energy input of ∼7.5 mWm⁻². The amount of denudation ranges from ∼18 km adjacent to the Alpine Fault to ∼2 km along the southeast margin of the Southern Alps; the late Cenozoic mean rate of denudation ranges from ∼2.5 mm/a at the Fault to ∼0.5 mm/a in the southeast parts of the Southern Alps. The amount of tectonic uplift decreases from ∼4 km at the Alpine Fault to ∼1 km along the eastern margin of the Southern Alps. 

The fission track data have been used to assess the role of faulting in the late Cenozoic uplift of the Pacific plate crust. For the Moonlight, Ostler, Harper, Torlesse, Porter's Pass and Hope faults, the vertical offset in all cases lies within the uncertainty of the data, typically ± 2 km, and is less than 30% of the surrounding uplift. Over a scale of kilometres the uplift is continuous and regular, and deformation in the plate boundary zone can therefore be treated as if it were ductile. 

The regression of the mean surface, summit, and valley elevations on the amount, age, and rate of uplift for each of 82 sample sites is used to establish the nature of the relationship between uplift and geomorphology. The preferred regression models have uniform slope but varying elevation response between transects. Uplift explains 80-90 % of the variation in elevation. Substitution of space for time has allowed the evolution of landforms to be studied. To the east of the Main Divide, elevation and relief are proportional to and closely related to the age of initiation of rock uplift and the amount of rock uplift (r²>0.8). Mean surface uplift was delayed for ∼2 Ma after the start of rock uplift, a result of the stripping of a soft cover rock succession that prior to rock uplift overlaid the harder greywacke basement. Under a rock uplift rate of 0.8 km/Ma, uplift of the mean surface proceeded at 0.4 km/Ma, while the summits increased in elevation at a rate of 0.6 km/Ma and valleys increased in elevation at 0.2 km/Ma. The mountains east of the Main Divide have continued to increase in elevation and relief and evolve in form over time since the start of uplift. Mountain elevation has little relationship with late Cenozoic mean rock uplift rates of 0.8-1.0 km/Ma or inferred contemporary rock uplift rates (r²∼0.3). In contrast, to the west of the Main Divide, elevation is shown to be closely related to rock uplift rate (r²>0.8). Transects with higher rock uplift rates support higher topography. Landforms are therefore in a stable equilibrium with rock uplift rate, and the landscape contains no residual evidence of the total amount of rock uplift, or the age of uplift. Lithological variation appears to have no relationship with elevation. 

The new uplift and geomorphic data allow the construction of a new model of the geomorphic evolution of the Southern Alps. The model quantifies the development over time and space of rock uplift, mean surface elevation, exhumation of crustal section, and relief. The earliest indications of mean surface uplift are between 4 and 5 Ma ago at the Alpine Fault. Mean surface uplift propagated southeastward from the Alpine Fault at a rate of 30 km/Ma. At 3 Ma ago greenschist was exposed in the southern parts of the Southern Alps near Lake Wanaka, and since then has become exhumed along a narrow strip east of the Alpine Fault. Amphibolite grade schist has been exhumed adjacent to the Alpine Fault only in the last 0.3 Ma. At the southeast margin of the Southern Alps a 1.0-1.5 km step in the basement topography separates the Southern Alps from the non-uplifted plains to the east. The existing models of the geomorphic development of the Southern Alps - the dynamic cuesta model of J. Adams [1980 and 1985] and the numerical model of Koons [1989] - are compared with the new data. Particular constraints unrealised by these two earlier models include: the earlier age of rock uplift (8 Ma ago) and its spatial variation (8 Ma ago to 3 Ma ago) across the Southern Alps; the lower long-term rock uplift rate (0.8- 1.0 mm/a) of the Southern Alps for most of the late Cenozoic; the lag between the start of rock uplift and the start of mean surface uplift; and the patterns of rock uplift and erosion across the Southern Alps. The age of the start of rock uplift, and the amount and rate of rock uplift, all of which vary spatially, are considered to be the dominant influences on the development of the landscape in the Southern Alps.

text: Uplift history and geomorphic development of the Southern Alps, New Zealand, assessed by fission track analysis The uplift history and geomorphic development of the Southern Alps has been studied, using fission track analysis of basement samples in combination with measurement of the present geomorphology of the Southern Alps. 

During the late Cenozoic the Pacific plate has been converging obliquely with the Australia plate in South Island, New Zealand. A result of this convergence has been the growth of a major mountain range - the Southern Alps - at the leading edge of the Pacific plate. The results of fission track analysis of 140 samples from 13 transects across the 300 km-long central sector of the Southern Alps reported here, establish the late Cenozoic vertical kinematics (amount, age, and rate of rock uplift) of the Pacific crust underlying the Southern Alps. The pattern of late Cenozoic rock uplift is asymmetrical with respect to the Alpine Fault, being a maximum (19 km) immediately east of the central part of the Fault, with lesser values at the eastern (3 km), northern (10 km) and southern (8 km) extremities of the Southern Alps. The age of the start of rock uplift varies spatially across the Southern Alps, the earliest indications from fission track analysis being at 8 Ma ago at the southern end of the Southern Alps, decreasing to 5 Ma ago at the northern end and 3 Ma ago along the southeastern margin. This age variation reflects the longer time over which the southern parts of the Southern Alps have been in collision. The rate of propagation of rock uplift southeastwards into the Pacific plate has been 30 mm/a, nearly 4 times the late Cenozoic average rate of convergence normal to the plate boundary. Late Cenozoic mean rock uplift rates range from a maximum of ∼2.8 mm/a at the Alpine Fault to a minimum of ∼1.0 mm/a in the east. Uplift has accelerated over time, but only significantly since 1.3 ± 0.3 Ma ago. 

The fission track data in combination with topographic data have been analysed to quantify the response of the surface of the Pacific plate to the late Cenozoic continent-continent collision. The rates of mean surface uplift, the rates of work done against gravity during the mountain building, and the erosional, isostatic and tectonic components (amounts and rates) of rock uplift, have been derived and mapped over the central 300 km length of the Southern Alps. The data do not support the notion of erosional-mechanical coupling of the two wedges in the two-sided orogen model of Koons [1990], but are consistent with overriding of the Australia plate by the Pacific plate. The late Cenozoic rate of mean surface uplift in the Southern Alps ranges from <0.1 mm/a adjacent to the Alpine Fault to >0.3 mm/a over most of the area east of the Main Divide. The highest rates of mean surface uplift do not coincide spatially with the regions of highest mean elevation. The rate of work done in elevating the mean surface ranges from ∼2.5 mWm⁻² to ∼10 mWm⁻², although most areas have experienced similar rates of energy input of ∼7.5 mWm⁻². The amount of denudation ranges from ∼18 km adjacent to the Alpine Fault to ∼2 km along the southeast margin of the Southern Alps; the late Cenozoic mean rate of denudation ranges from ∼2.5 mm/a at the Fault to ∼0.5 mm/a in the southeast parts of the Southern Alps. The amount of tectonic uplift decreases from ∼4 km at the Alpine Fault to ∼1 km along the eastern margin of the Southern Alps. 

The fission track data have been used to assess the role of faulting in the late Cenozoic uplift of the Pacific plate crust. For the Moonlight, Ostler, Harper, Torlesse, Porter's Pass and Hope faults, the vertical offset in all cases lies within the uncertainty of the data, typically ± 2 km, and is less than 30% of the surrounding uplift. Over a scale of kilometres the uplift is continuous and regular, and deformation in the plate boundary zone can therefore be treated as if it were ductile. 

The regression of the mean surface, summit, and valley elevations on the amount, age, and rate of uplift for each of 82 sample sites is used to establish the nature of the relationship between uplift and geomorphology. The preferred regression models have uniform slope but varying elevation response between transects. Uplift explains 80-90 % of the variation in elevation. Substitution of space for time has allowed the evolution of landforms to be studied. To the east of the Main Divide, elevation and relief are proportional to and closely related to the age of initiation of rock uplift and the amount of rock uplift (r²>0.8). Mean surface uplift was delayed for ∼2 Ma after the start of rock uplift, a result of the stripping of a soft cover rock succession that prior to rock uplift overlaid the harder greywacke basement. Under a rock uplift rate of 0.8 km/Ma, uplift of the mean surface proceeded at 0.4 km/Ma, while the summits increased in elevation at a rate of 0.6 km/Ma and valleys increased in elevation at 0.2 km/Ma. The mountains east of the Main Divide have continued to increase in elevation and relief and evolve in form over time since the start of uplift. Mountain elevation has little relationship with late Cenozoic mean rock uplift rates of 0.8-1.0 km/Ma or inferred contemporary rock uplift rates (r²∼0.3). In contrast, to the west of the Main Divide, elevation is shown to be closely related to rock uplift rate (r²>0.8). Transects with higher rock uplift rates support higher topography. Landforms are therefore in a stable equilibrium with rock uplift rate, and the landscape contains no residual evidence of the total amount of rock uplift, or the age of uplift. Lithological variation appears to have no relationship with elevation. 

The new uplift and geomorphic data allow the construction of a new model of the geomorphic evolution of the Southern Alps. The model quantifies the development over time and space of rock uplift, mean surface elevation, exhumation of crustal section, and relief. The earliest indications of mean surface uplift are between 4 and 5 Ma ago at the Alpine Fault. Mean surface uplift propagated southeastward from the Alpine Fault at a rate of 30 km/Ma. At 3 Ma ago greenschist was exposed in the southern parts of the Southern Alps near Lake Wanaka, and since then has become exhumed along a narrow strip east of the Alpine Fault. Amphibolite grade schist has been exhumed adjacent to the Alpine Fault only in the last 0.3 Ma. At the southeast margin of the Southern Alps a 1.0-1.5 km step in the basement topography separates the Southern Alps from the non-uplifted plains to the east. The existing models of the geomorphic development of the Southern Alps - the dynamic cuesta model of J. Adams [1980 and 1985] and the numerical model of Koons [1989] - are compared with the new data. Particular constraints unrealised by these two earlier models include: the earlier age of rock uplift (8 Ma ago) and its spatial variation (8 Ma ago to 3 Ma ago) across the Southern Alps; the lower long-term rock uplift rate (0.8- 1.0 mm/a) of the Southern Alps for most of the late Cenozoic; the lag between the start of rock uplift and the start of mean surface uplift; and the patterns of rock uplift and erosion across the Southern Alps. The age of the start of rock uplift, and the amount and rate of rock uplift, all of which vary spatially, are considered to be the dominant influences on the development of the landscape in the Southern Alps.

year: 1992

title: Hone Werahiko: the discoverer of gold at Te Aroha

authors: Hart, Philip

abstract: Originally Hone Kahukahu, when he was living at Ohinemutu in the 1860s he became known as Hone Werahiko, an Arawa name he retained for the rest of his life. His father, a member of Ngati Kahungungu, had been captured by Arawa; his mother was a Waikato. A widow living at Maketu chose him as her second husband because he was ‘a good looking fellow & understood English’. 
In the late 1860s and much of the 1870s, he prospected in Hauraki and even in the King Country, and worked underground in a Thames mine, the only Maori known to have done so. But in the early 1870s he gave up mining to be a pioneer publican and storekeeper at Ohinemutu, at Rotorua. He acquired land and property there, but after his wife died he returned to prospecting full-time. 
Werahiko’s first investigation of Te Aroha was in 1877, when he was ordered off by the local hapu. He returned in 1880 as the head of a prospecting party subsidized by the government. After finding gold, he was granted the Prospectors’ Claim and, in due course, a reward, and for a time supervised its development. Investing in other claims, he traded in shares. When his discovery turned out to be a duffer, he explored other parts of the mountain, first having high hopes for the Tui portion but then, after four months of exploring over winter with the support of three other Maori, he announced the discovery of his New Find at Waiorongomai. Once again he acquired partners, mostly Paheka, and traded in shares, and for some time supervised the opening up of his new find.
Later, he was invited to prospect the King Country, but this did not eventuate. His last involvement in mining was at Karangahake. Because of the hardships of his prospecting at Te Aroha, he died at an early age, leaving a young second wife. His memory lived on, amongst Pakeha miners in particular, because he had the rare distinction for a prospector of being regarded as totally honest, and he was admired for succeeding when so many others had failed.

[Note: Especially when he first came to public attention, many Pakeha struggled with Hone Werahiko’s name, which was recorded in a variety of incorrect forms, the worst example being Hoani Whaekareka.  Even the warden at first gave his name as Hone Wharekino.  Many Pakeha found it simpler to refer to him as ‘Johnny the Maori’.  In this paper, his name is given correctly throughout.]

text: Hone Werahiko: the discoverer of gold at Te Aroha Originally Hone Kahukahu, when he was living at Ohinemutu in the 1860s he became known as Hone Werahiko, an Arawa name he retained for the rest of his life. His father, a member of Ngati Kahungungu, had been captured by Arawa; his mother was a Waikato. A widow living at Maketu chose him as her second husband because he was ‘a good looking fellow & understood English’. 
In the late 1860s and much of the 1870s, he prospected in Hauraki and even in the King Country, and worked underground in a Thames mine, the only Maori known to have done so. But in the early 1870s he gave up mining to be a pioneer publican and storekeeper at Ohinemutu, at Rotorua. He acquired land and property there, but after his wife died he returned to prospecting full-time. 
Werahiko’s first investigation of Te Aroha was in 1877, when he was ordered off by the local hapu. He returned in 1880 as the head of a prospecting party subsidized by the government. After finding gold, he was granted the Prospectors’ Claim and, in due course, a reward, and for a time supervised its development. Investing in other claims, he traded in shares. When his discovery turned out to be a duffer, he explored other parts of the mountain, first having high hopes for the Tui portion but then, after four months of exploring over winter with the support of three other Maori, he announced the discovery of his New Find at Waiorongomai. Once again he acquired partners, mostly Paheka, and traded in shares, and for some time supervised the opening up of his new find.
Later, he was invited to prospect the King Country, but this did not eventuate. His last involvement in mining was at Karangahake. Because of the hardships of his prospecting at Te Aroha, he died at an early age, leaving a young second wife. His memory lived on, amongst Pakeha miners in particular, because he had the rare distinction for a prospector of being regarded as totally honest, and he was admired for succeeding when so many others had failed.

[Note: Especially when he first came to public attention, many Pakeha struggled with Hone Werahiko’s name, which was recorded in a variety of incorrect forms, the worst example being Hoani Whaekareka.  Even the warden at first gave his name as Hone Wharekino.  Many Pakeha found it simpler to refer to him as ‘Johnny the Maori’.  In this paper, his name is given correctly throughout.]

year: 2016